Advanced search
Publication Cover
Stochastics and Stochastic Reports Volume 61, 1997 - Issue 3-4
Journal homepage
659
Views
126
CrossRef citations to date
0
Altmetric
Original Articles

On stochastic convolution in banach spaces and applications

Zdzisław Brzeźniak Department of Pure Mathematics, The University of Hull, Hull, HU6 7RX, UK
Pages 245-295 | Published online: 04 Apr 2007

Citations (126)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (7)

K. Kinra & M. T. Mohan. (2023) Existence and upper semicontinuity of random attractors for the 2D stochastic convective Brinkman–Forchheimer equations in bounded domains. Stochastics 95:6, pages 1042-1077.
Read now
Sonja Cox & Erika Hausenblas. (2012) Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noise. International Journal of Computer Mathematics 89:18, pages 2460-2478.
Read now
Szymon Peszat & Samy Tindel. (2010) Stochastic Heat and Wave Equations on a Lie Group. Stochastic Analysis and Applications 28:4, pages 662-695.
Read now
Erika Hausenblas & Jan Seidler. (2007) Stochastic Convolutions Driven by Martingales: Maximal Inequalities and Exponential Integrability. Stochastic Analysis and Applications 26:1, pages 98-119.
Read now
Johanna Dettweiler, Lutz Weis & Jan van Neerven. (2006) Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem. Stochastic Analysis and Applications 24:4, pages 843-869.
Read now
Marc Barton-Smith. (2004) Global Solution for a Stochastic Ginzburg-Landau Equation with Multiplicative Noise. Stochastic Analysis and Applications 22:1, pages 1-18.
Read now
A. de Bouard & A. Debussche. (2003) The Stochastic Nonlinear Schrödinger Equation in H 1 . Stochastic Analysis and Applications 21:1, pages 97-126.
Read now

Articles from other publishers (119)

Chenjie Fan, Weijun Xu & Zehua Zhao. (2023) Long Time Behavior of Stochastic NLS with a Small Multiplicative Noise. Communications in Mathematical Physics 404:1, pages 563-595.
Crossref
Kush Kinra & Manil T. Mohan. (2021) Large Time Behavior of Deterministic and Stochastic 3D Convective Brinkman-Forchheimer Equations in Periodic Domains. Journal of Dynamics and Differential Equations 35:3, pages 2355-2396.
Crossref
Yong Chen, Jinqiao Duan & Hongjun Gao. (2023) Well-posedness and wave-breaking for the stochastic rotation-two-component Camassa–Holm system. The Annals of Applied Probability 33:4.
Crossref
Rangrang Zhang. (2022) On the Small Time Asymptotics of Quasilinear Parabolic Stochastic Partial Differential Equations. Potential Analysis 59:2, pages 467-495.
Crossref
Florian Bechtold. (2021) Strong solutions of semilinear SPDEs with unbounded diffusion. Stochastics and Partial Differential Equations: Analysis and Computations 11:1, pages 1-30.
Crossref
Qiang Li & Lishan Liu. (2023) Existence and asymptotic behavior of square-mean $ S $-asymptotically periodic solutions of fractional stochastic evolution equations. Discrete and Continuous Dynamical Systems - S 0:0, pages 0-0.
Crossref
Zdzisław Brzeźniak & Nimit Rana. (2022) Local solution to an energy critical 2-D stochastic wave equation with exponential nonlinearity in a bounded domain. Journal of Differential Equations 340, pages 386-462.
Crossref
Hermano Frid, Yachun Li, Daniel Marroquin, João F. C. Nariyoshi & Zirong Zeng. (2021) The strong trace property and the Neumann problem for stochastic conservation laws. Stochastics and Partial Differential Equations: Analysis and Computations 10:4, pages 1392-1450.
Crossref
Antonio Agresti & Mark Veraar. (2022) Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence*. Nonlinearity 35:8, pages 4100-4210.
Crossref
Jan van Neerven & Mark Veraar. (2021) Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes. Stochastics and Partial Differential Equations: Analysis and Computations 10:2, pages 516-581.
Crossref
Antonio Agresti & Mark Veraar. (2022) Nonlinear parabolic stochastic evolution equations in critical spaces part II. Journal of Evolution Equations 22:2.
Crossref
Jérôme Droniou, Beniamin Goldys & Kim-Ngan Le. (2022) Design and convergence analysis of numerical methods for stochastic evolution equations with Leray–Lions operator. IMA Journal of Numerical Analysis 42:2, pages 1143-1179.
Crossref
B. Juarez-Campos, E. I. Kaikina & A. V. Vázquez-Esquivel. (2022) Stochastic Ginzburg–Landau equation on a half-line driven by the multiplicative noise. Journal of Mathematical Physics 63:4.
Crossref
Erika Hausenblas, Debopriya Mukherjee & Thanh Tran. (2022) The one-dimensional stochastic Keller–Segel model with time-homogeneous spatial Wiener processes. Journal of Differential Equations 310, pages 506-554.
Crossref
Chenjie Fan & Weijun Xu. (2021) Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on ℝ at L2 regularity. Analysis & PDE 14:8, pages 2561-2594.
Crossref
Zdzisław Brzeźniak & Jakub Slavík. (2021) Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise. Journal of Differential Equations 296, pages 617-676.
Crossref
T. E. Govindan. (2021) Trotter-Kato approximations of stochastic neutral partial functional differential equations. Indian Journal of Pure and Applied Mathematics 52:3, pages 822-836.
Crossref
Emiel Lorist & Mark Veraar. (2021) Singular stochastic integral operators. Analysis & PDE 14:5, pages 1443-1507.
Crossref
Anne De Bouard, Antoine Hocquet & Andreas Prohl. (2021) Existence, uniqueness and regularity for the stochastic Ericksen–Leslie equation. Nonlinearity 34:6, pages 4057-4114.
Crossref
Chenjie Fan & Weijun Xu. (2020) Decay of the stochastic linear Schrödinger equation in $$d \ge 3$$ with small multiplicative noise. Stochastics and Partial Differential Equations: Analysis and Computations 9:2, pages 472-490.
Crossref
Chong Liu, David J. Prömel & Josef Teichmann. (2020) Stochastic analysis with modelled distributions. Stochastics and Partial Differential Equations: Analysis and Computations 9:2, pages 343-379.
Crossref
Arnulf Jentzen & Ryan Kurniawan. (2020) Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients. Foundations of Computational Mathematics 21:2, pages 445-536.
Crossref
Adam Andersson, Arnulf Jentzen & Ryan Kurniawan. (2021) Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values. Journal of Mathematical Analysis and Applications 495:1, pages 124558.
Crossref
Tôn Việt Tạ. (2021) Strict solutions to stochastic semilinear evolution equations in M-type 2 Banach spaces. Communications on Pure & Applied Analysis 20:5, pages 1867.
Crossref
Chenjie Fan & Weijun Xu. (2021) A Wong--Zakai Theorem for the Stochastic Mass-critical Nonlinear Schrödinger Equation. SIAM Journal on Mathematical Analysis 53:3, pages 3681-3715.
Crossref
Jan van Neerven & Mark Veraar. (2020) Maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378:2185, pages 20190622.
Crossref
Nikos I. Kavallaris & Yubin Yan. (2020) Finite-time blow-up of a non-local stochastic parabolic problem. Stochastic Processes and their Applications 130:9, pages 5605-5635.
Crossref
Martin Ondreját & Mark Veraar. (2020) On temporal regularity of stochastic convolutions in $2$-smooth Banach spaces. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56:3.
Crossref
Charles-Edouard Bréhier. (2020) Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component. Stochastic Processes and their Applications 130:6, pages 3325-3368.
Crossref
Zhihui Liu & Zhonghua Qiao. (2020) Strong approximation of monotone stochastic partial differential equations driven by white noise. IMA Journal of Numerical Analysis 40:2, pages 1074-1093.
Crossref
Antonio Agresti & Mark Veraar. (2020) Stability properties of stochastic maximal L-regularity. Journal of Mathematical Analysis and Applications 482:2, pages 123553.
Crossref
Diego Alonso-Orán & Aythami Bethencourt de León. (2019) On the Well-Posedness of Stochastic Boussinesq Equations with Transport Noise. Journal of Nonlinear Science 30:1, pages 175-224.
Crossref
Weicong Su. (2020) On the peaks of a stochastic heat equation on a sphere with a large radius. Electronic Journal of Probability 25:none.
Crossref
Lihuai Du & Ting Zhang. (2020) Local and global strong solutions to the stochastic incompressible Navier-Stokes equations in critical Besov space. Journal of Mathematical Analysis and Applications 481:1, pages 123472.
Crossref
Pierre Portal & Mark Veraar. (2019) Stochastic maximal regularity for rough time-dependent problems. Stochastics and Partial Differential Equations: Analysis and Computations 7:4, pages 541-597.
Crossref
Giuseppe Da Prato, Arnulf Jentzen & Michael Röckner. (2019) A mild Itô formula for SPDEs. Transactions of the American Mathematical Society 372:6, pages 3755-3807.
Crossref
Jialin Hong, Chuying Huang & Zhihui Liu. (2019) Optimal regularity of stochastic evolution equations in M-type 2 Banach spaces. Journal of Differential Equations 267:3, pages 1955-1971.
Crossref
Daniel Conus, Arnulf Jentzen & Ryan Kurniawan. (2019) Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients. The Annals of Applied Probability 29:2.
Crossref
Adam Bobrowski & Markus Kunze. (2019) Irregular convergence of mild solutions of semilinear equations. Journal of Mathematical Analysis and Applications 472:2, pages 1401-1419.
Crossref
Sandra Cerrai & Arnaud Debussche. (2019) Large deviations for the two-dimensional stochastic Navier–Stokes equation with vanishing noise correlation. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55:1.
Crossref
Luca Hornung. (2018) Quasilinear Parabolic Stochastic Evolution Equations Via Maximal Lp-Regularity. Potential Analysis 50:2, pages 279-326.
Crossref
N. U. Ahmed. (2019) Partially Observed Stochastic Evolution Equations on Banach Spaces and Their Optimal Lipschitz Feedback Control Law. SIAM Journal on Control and Optimization 57:5, pages 3101-3117.
Crossref
Zdzisław Brzeźniak & Elżbieta Motyl. (2019) Fractionally Dissipative Stochastic Quasi-Geostrophic Type Equations on ${\mathbb{R}}^{d}$. SIAM Journal on Mathematical Analysis 51:3, pages 2306-2358.
Crossref
Charles-Edouard Bréhier & Arnaud Debussche. (2018) Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient. Journal de Mathématiques Pures et Appliquées 119, pages 193-254.
Crossref
Zdzisław Brzeźniak & Tayfun Kok. (2018) Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations. Finance and Stochastics 22:4, pages 959-1006.
Crossref
Petru A. Cioica-Licht, Kyeong-Hun Kim, Kijung Lee & Felix Lindner. (2017) An $$L_{p}$$ L p -estimate for the stochastic heat equation on an angular domain in $$\mathbb {R}^2$$ R 2. Stochastics and Partial Differential Equations: Analysis and Computations 6:1, pages 45-72.
Crossref
Z. Brzeźniak, B. Goldys & Q. T. Le Gia. (2017) Random Attractors for the Stochastic Navier–Stokes Equations on the 2D Unit Sphere. Journal of Mathematical Fluid Mechanics 20:1, pages 227-253.
Crossref
Martina Hofmanová & Tusheng Zhang. (2017) Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness. Stochastic Processes and their Applications 127:10, pages 3354-3371.
Crossref
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan & Timo Welti. (2017) On the differentiability of solutions of stochastic evolution equations with respect to their initial values. Nonlinear Analysis 162, pages 128-161.
Crossref
Manil T. Mohan & Sivaguru S. Sritharan. (2017) Stochastic quasilinear evolution equations in UMD Banach spaces. Mathematische Nachrichten 290:13, pages 1971-1990.
Crossref
Martina Hofmanová, Matthias Röger & Max von Renesse. (2016) Weak solutions for a stochastic mean curvature flow of two-dimensional graphs. Probability Theory and Related Fields 168:1-2, pages 373-408.
Crossref
Zdzisław Brzeźniak & Benedetta Ferrario. (2016) A note on stochastic Navier–Stokes equations with not regular multiplicative noise. Stochastics and Partial Differential Equations: Analysis and Computations 5:1, pages 53-80.
Crossref
Roland Schnaubelt & Mark Veraar. (2016) Regularity of stochastic Volterra equations by functional calculus methods. Journal of Evolution Equations 17:1, pages 523-536.
Crossref
Tôn Việt Tạ. (2017) Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity. Discrete & Continuous Dynamical Systems - A 37:8, pages 4507-4542.
Crossref
Paul André Razafimandimby & Zdzisław Brzeźniak. (2016) Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces. Discrete and Continuous Dynamical Systems - Series B 21:4, pages 1051-1077.
Crossref
Mark Veraar & Ivan Yaroslavtsev. (2016) Cylindrical continuous martingales and stochastic integration in infinite dimensions. Electronic Journal of Probability 21:none.
Crossref
Dominic Breit & Martina Hofmanová. (2016) On time regularity of stochastic evolution equations with monotone coefficients. Comptes Rendus Mathematique 354:1, pages 33-37.
Crossref
Rafael Serrano. (2015) A note on space–time Hölder regularity of mild solutions to stochastic Cauchy problems in $L^{p}$-spaces. Brazilian Journal of Probability and Statistics 29:4.
Crossref
Paul André Razafimandimby & Mamadou Sango. (2015) Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations. Zeitschrift für angewandte Mathematik und Physik 66:5, pages 2197-2235.
Crossref
Z. Brzeźniak, S. Cerrai & M. Freidlin. (2014) Quasipotential and exit time for 2D Stochastic Navier-Stokes equations driven by space time white noise. Probability Theory and Related Fields 162:3-4, pages 739-793.
Crossref
Z. Brzeźniak, B. Goldys & Q.T. Le Gia. (2015) Random dynamical systems generated by stochastic Navier–Stokes equations on a rotating sphere. Journal of Mathematical Analysis and Applications 426:1, pages 505-545.
Crossref
Jan van Neerven, Mark Veraar & Lutz Weis. (2014) On the $$R$$ R -boundedness of stochastic convolution operators. Positivity 19:2, pages 355-384.
Crossref
Michael Röckner, Rongchan Zhu & Xiangchan Zhu. (2015) Sub and supercritical stochastic quasi-geostrophic equation. The Annals of Probability 43:3.
Crossref
Arnaud Debussche, Sylvain De Moor & Julien Vovelle. (2015) Diffusion limit for the radiative transfer equation perturbed by a Wiener process. Kinetic & Related Models 8:3, pages 467-492.
Crossref
Arnaud Debussche, Sylvain de Moor & Martina Hofmanová. (2015) A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type. SIAM Journal on Mathematical Analysis 47:2, pages 1590-1614.
Crossref
E. Issoglio & M. Riedle. (2014) Cylindrical fractional Brownian motion in Banach spaces. Stochastic Processes and their Applications 124:11, pages 3507-3534.
Crossref
Le Chen & Robert C. Dalang. (2014) Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions. Stochastic Partial Differential Equations: Analysis and Computations 2:3, pages 316-352.
Crossref
Z. Brzeźniak & A. Millet. (2013) On the Stochastic Strichartz Estimates and the Stochastic Nonlinear Schrödinger Equation on a Compact Riemannian Manifold. Potential Analysis 41:2, pages 269-315.
Crossref
Michael Röckner, Rongchan Zhu & Xiangchan Zhu. (2014) A note on stochastic semilinear equations and their associated Fokker–Planck equations. Journal of Mathematical Analysis and Applications 415:1, pages 83-109.
Crossref
Xiangjun Wang & Guo Jiang. (2014) -strong solutions of stochastic partial differential equations with monotonic drifts . Journal of Mathematical Analysis and Applications 415:1, pages 178-203.
Crossref
Paul Crewe. (2014) Infinitely delayed stochastic evolution equations on UMD Banach spaces. Journal of Mathematical Analysis and Applications 415:1, pages 325-345.
Crossref
S. Perkins & D.S. Leslie. (2014) Stochastic fictitious play with continuous action sets. Journal of Economic Theory 152, pages 179-213.
Crossref
Rongchan Zhu & Xiangchan Zhu. (2014) Martingale solutions for stochastic active scalar equations perturbed by non-trace class noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics 17:02, pages 1450010.
Crossref
Matthijs Pronk & Mark Veraar. (2014) A new approach to stochastic evolution equations with adapted drift. Journal of Differential Equations 256:11, pages 3634-3683.
Crossref
Zdzisław Brzeźniak, Ben Goldys & Misha Neklyudov. (2014) Multidimensional Stochastic Burgers Equation. SIAM Journal on Mathematical Analysis 46:1, pages 871-889.
Crossref
Sonja Gisela Cox & Erika Hausenblas. (2013) A perturbation result for semi-linear stochastic differential equations in UMD Banach spaces. Journal of Evolution Equations 13:4, pages 795-827.
Crossref
Martina Hofmanová. (2012) Strong solutions of semilinear stochastic partial differential equations. Nonlinear Differential Equations and Applications NoDEA 20:3, pages 757-778.
Crossref
Zdzisław Brzeźniak & Martin Ondreját. (2013) Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces. The Annals of Probability 41:3B.
Crossref
Shao-Qin Zhang. (2013) Harnack inequality for semilinear SPDE with multiplicative noise. Statistics & Probability Letters 83:4, pages 1184-1192.
Crossref
Zdzisław Brzeźniak & Rafael Serrano. (2013) Optimal Relaxed Control of Dissipative Stochastic Partial Differential Equations in Banach Spaces. SIAM Journal on Control and Optimization 51:3, pages 2664-2703.
Crossref
Markus Kunze & Jan van Neerven. (2012) Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations. Journal of Differential Equations 253:3, pages 1036-1068.
Crossref
A. Deya, M. Gubinelli & S. Tindel. (2011) Non-linear rough heat equations. Probability Theory and Related Fields 153:1-2, pages 97-147.
Crossref
Jan van Neerven, Mark Veraar & Lutz Weis. (2012) Stochastic maximal Lp-regularity. The Annals of Probability 40:2.
Crossref
Zdzisław Brzeźniak, Jan van Neerven & Donna Salopek. (2012) Stochastic evolution equations driven by Liouville fractional Brownian motion. Czechoslovak Mathematical Journal 62:1, pages 1-27.
Crossref
Jan van Neerven, Mark Veraar & Lutz Weis. (2012) Maximal $L^p$-Regularity for Stochastic Evolution Equations. SIAM Journal on Mathematical Analysis 44:3, pages 1372-1414.
Crossref
Arnulf Jentzen & Michael Röckner. (2012) Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise. Journal of Differential Equations 252:1, pages 114-136.
Crossref
Mark Veraar & Lutz Weis. (2011) A note on maximal estimates for stochastic convolutions. Czechoslovak Mathematical Journal 61:3, pages 743-758.
Crossref
Markus Kunze & Jan van Neerven. (2011) Approximating the coefficients in semilinear stochastic partial differential equations. Journal of Evolution Equations 11:3, pages 577-604.
Crossref
Sonja Cox & Mark Veraar. (2011) Vector-valued decoupling and the Burkholder–Davis–Gundy inequality. Illinois Journal of Mathematics 55:1.
Crossref
Wolfgang Desch & Stig-Olof Londen. 2011. Parabolic Problems. Parabolic Problems 131 166 .
Roland Schnaubelt & Mark Veraar. 2011. Parabolic Problems. Parabolic Problems 609 629 .
Jan Maas & Jan van Neerven. 2011. Parabolic Problems. Parabolic Problems 463 477 .
Zdzisław Brzeźniak, Hongwei Long & Isabel Simão. (2010) Invariant measures for stochastic evolution equations in M-type 2 Banach spaces. Journal of Evolution Equations 10:4, pages 785-810.
Crossref
Mark C. Veraar. (2009) Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations. Journal of Evolution Equations 10:1, pages 85-127.
Crossref
Xicheng Zhang. (2010) Stochastic Volterra equations in Banach spaces and stochastic partial differential equation. Journal of Functional Analysis 258:4, pages 1361-1425.
Crossref
Zdzisław Brzeźniak & Jerzy Zabczyk. (2009) Regularity of Ornstein–Uhlenbeck Processes Driven by a Lévy White Noise. Potential Analysis 32:2, pages 153-188.
Crossref
Jan Seidler. (2010) Exponential Estimates for Stochastic Convolutions in 2-Smooth Banach Spaces. Electronic Journal of Probability 15:none.
Crossref
Sonja Cox & Jan van Neerven. (2010) Convergence Rates of the Splitting Scheme for Parabolic Linear Stochastic Cauchy Problems. SIAM Journal on Numerical Analysis 48:2, pages 428-451.
Crossref
XICHENG ZHANG. (2011) ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS. Stochastics and Dynamics 09:04, pages 549-595.
Crossref
Zdzisław Brzeźniak & Erika Hausenblas. (2008) Maximal regularity for stochastic convolutions driven by Lévy processes. Probability Theory and Related Fields 145:3-4, pages 615-637.
Crossref
S. Albeverio, V. Mandrekar & B. Rüdiger. (2009) Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise. Stochastic Processes and their Applications 119:3, pages 835-863.
Crossref
Yuhong Li. (2008) ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS*. Journal of Systems Science and Complexity 21:3, pages 416-426.
Crossref
J.M.A.M. van Neerven, M.C. Veraar & L. Weis. (2008) Stochastic evolution equations in UMD Banach spaces. Journal of Functional Analysis 255:4, pages 940-993.
Crossref
Li Yuhong, Zdzisław Brzeźniak & Zhou Jianzhong. (2008) Conceptual Analysis and Random Attractor for Dissipative Random Dynamical Systems. Acta Mathematica Scientia 28:2, pages 253-268.
Crossref
Nicolai V. Krylov. 2008. Topics in Stochastic Analysis and Nonparametric Estimation. Topics in Stochastic Analysis and Nonparametric Estimation 151 197 .
Martin Ondreját. (2007) Uniqueness for stochastic non-linear wave equations. Nonlinear Analysis: Theory, Methods & Applications 67:12, pages 3287-3310.
Crossref
MARTIN ONDREJÁT. (2012) INTEGRAL REPRESENTATIONS OF CYLINDRICAL LOCAL MARTINGALES IN EVERY SEPARABLE BANACH SPACE. Infinite Dimensional Analysis, Quantum Probability and Related Topics 10:03, pages 365-379.
Crossref
Xicheng Zhang. (2007) Regularities for semilinear stochastic partial differential equations. Journal of Functional Analysis 249:2, pages 454-476.
Crossref
J. M. A. M. van Neerven, M. C. Veraar & L. Weis. (2007) Stochastic integration in UMD Banach spaces. The Annals of Probability 35:4.
Crossref
Xicheng Zhang. (2006) -Theory of semi-linear SPDEs on general measure spaces and applications . Journal of Functional Analysis 239:1, pages 44-75.
Crossref
Martin Ondrejat. (2005) Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces. Czechoslovak Mathematical Journal 55:4, pages 1003-1039.
Crossref
Arnaud Debussche & Anne de Bouard. (2005) Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise. The Annals of Probability 33:3.
Crossref
Zdzisław Brzeźniak, Bohdan Maslowski & Jan Seidler. (2004) Stochastic nonlinear beam equations. Probability Theory and Related Fields 132:1, pages 119-149.
Crossref
Erika Hausenblas. (2005) Existence, Uniqueness and Regularity of Parabolic SPDEs Driven by Poisson Random Measure. Electronic Journal of Probability 10:none.
Crossref
Erika Hausenblas. (2002) Numerical analysis of semilinear stochastic evolution equations in Banach spaces. Journal of Computational and Applied Mathematics 147:2, pages 485-516.
Crossref
Szymon Peszat. 2002. Stochastic partial differential equations and applications. Stochastic partial differential equations and applications 417 427 .
M. Ledoux, T. Lyons & Z. Qian. (2002) Lévy area of Wiener processes in Banach spaces. The Annals of Probability 30:2.
Crossref
Zdzislaw Brzezniak & Szymon Peszat. (2001) Stochastic two dimensional euler equations. The Annals of Probability 29:4.
Crossref
Zdzisław Brzeźniak & Dariusz Ga̧tarek. (1999) Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces. Stochastic Processes and their Applications 84:2, pages 187-225.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.