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Stochastic Analysis and Applications Volume 23, 2005 - Issue 2
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Original Articles

Stochastic Integrals and the Lévy–Ito Decomposition Theorem on Separable Banach Spaces

S. Albeverio Institut für Angewandte Mathematik, Abteilung Stochastik and SFB6M, Universität Bonn, Bonn, Germany
&
B. Rüdiger# Mathematisches Institut, Universität Koblenz–Landau, Koblenz, BonnCorrespondence[email protected]
Pages 217-253 | Published online: 07 Sep 2017

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Thilo Meyer-Brandis. (2008) Differential equations driven by Lévy white noise in spaces of Hilbert space-valued stochastic distributions. Stochastics 80:4, pages 371-396.
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B. Rüdiger & G. Ziglio. (2006) Itô formula for stochastic integrals w.r.t. compensated Poisson random measures on separable Banach spaces. Stochastics 78:6, pages 377-410.
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V. Mandrekar & B. Rüdiger. (2006) Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces. Stochastics 78:4, pages 189-212.
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Articles from other publishers (29)

Gerardo Barrera, Michael A. Högele & Juan Carlos Pardo. (2022) The cutoff phenomenon for the stochastic heat and wave equation subject to small Lévy noise. Stochastics and Partial Differential Equations: Analysis and Computations 11:3, pages 1164-1202.
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Shufen Zhao, Xiaoqian Li & Jianzhong Zhang. (2023) S-asymptotically $ \omega $-periodic solutions in distribution for a class of stochastic fractional functional differential equations. Electronic Research Archive 31:2, pages 599-614.
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V. Mandrekar & B. Rüdiger. 2023. Quantum and Stochastic Mathematical Physics. Quantum and Stochastic Mathematical Physics 295 313 .
C. A. Fonseca-Mora. (2022) Stochastic evolution equations with Lévy noise in the dual of a nuclear space. Stochastics and Partial Differential Equations: Analysis and Computations.
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Shangzhi Li & Shangjiang Guo. (2022) Invariant measures and random attractors of stochastic delay differential equations in Hilbert space. Electronic Journal of Qualitative Theory of Differential Equations:56, pages 1-25.
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Alessandra Lunardi & Michael Röckner. (2021) Schauder theorems for a class of (pseudo‐)differential operators on finite‐ and infinite‐dimensional state spaces. Journal of the London Mathematical Society 104:2, pages 492-540.
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Zhi Li, Liping Xu & Litan Yan. (2021) Global attracting set, exponential stability and stability in distribution of SPDEs with jumps. Nonlinear Analysis: Hybrid Systems 41, pages 101056.
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Anddy E. Alvarado-Solano & Christian A. Fonseca-Mora. (2021) Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures. Latin American Journal of Probability and Mathematical Statistics 18:1, pages 1267.
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Benjamin Gess, Wei Liu & Andre Schenke. (2020) Random attractors for locally monotone stochastic partial differential equations. Journal of Differential Equations 269:4, pages 3414-3455.
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Ivan S. Yaroslavtsev. (2019) Martingale decompositions and weak differential subordination in UMD Banach spaces. Bernoulli 25:3.
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R. Mabel Lizzy, K. Balachandran & Yong-Ki Ma. (2019) Controllability of Nonlinear Stochastic Fractional Higher Order Dynamical Systems. Fractional Calculus and Applied Analysis 22:4, pages 1063-1085.
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Sergio Albeverio, Leszek Gawarecki, Vidyadhar Mandrekar, Barbara Rüdiger & Barun Sarkar. (2017) Itô formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties. Random Operators and Stochastic Equations 25:2, pages 79-105.
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Sergio Albeverio, Luca Di Persio, Elisa Mastrogiacomo & Boubaker Smii. (2016) A Class of Lévy Driven SDEs and their Explicit Invariant Measures. Potential Analysis 45:2, pages 229-259.
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BYOUNG JIN CHOI, JIN PIL CHOI & UN CIG JI. (2016) STOCHASTIC INTEGRAL OF PROCESSES TAKING VALUES OF GENERALIZED OPERATORS. Journal of applied mathematics & informatics 34:1_2, pages 167-178.
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T. E. GovindanT. E. Govindan. 2016. Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications. Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications 11 68 .
Sergio Albeverio & Boubaker Smii. (2015) Asymptotic expansions for SDE’s with small multiplicative noise. Stochastic Processes and their Applications 125:3, pages 1009-1031.
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David Applebaum. (2015) Infinite dimensional Ornstein-Uhlenbeck processes driven by Lévy processes. Probability Surveys 12:none.
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Sergio Albeverio, Elisa Mastrogiacomo & Boubaker Smii. (2013) Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise. Stochastic Processes and their Applications 123:6, pages 2084-2109.
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Bijan Z. Zangeneh. 2013. Malliavin Calculus and Stochastic Analysis. Malliavin Calculus and Stochastic Analysis 315 331 .
Bin Xie. (2011) Uniqueness of Invariant Measures of Infinite Dimensional Stochastic Differential Equations Driven by Lévy Noises. Potential Analysis 36:1, pages 35-66.
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Florian Kn?ble. (2011) Ornstein?Uhlenbeck equations with time-dependent coefficients and L?vy noise in finite and infinite dimensions. Journal of Evolution Equations 11:4, pages 959-993.
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Erika Hausenblas. (2010) Maximal Inequalities of the Itô Integral with Respect to Poisson Random Measures or Lévy Processes on Banach Spaces. Potential Analysis 35:3, pages 223-251.
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Kai Liu. (2010) Retarded Stationary Ornstein–Uhlenbeck Processes Driven by Lévy Noise and Operator Self-Decomposability. Potential Analysis 33:3, pages 291-312.
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Markus Riedle & Onno van Gaans. (2009) Stochastic integration for Lévy processes with values in Banach spaces. Stochastic Processes and their Applications 119:6, pages 1952-1974.
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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.
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Jiaowan Luo & Kai Liu. (2008) Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps. Stochastic Processes and their Applications 118:5, pages 864-895.
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S. Albeverio, Yu. M. Berezansky & V. A. Tesko. (2007) A generalization of an extended stochastic integral. Ukrainian Mathematical Journal 59:5, pages 645-677.
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David Applebaum. (2006) On the Infinitesimal Generators of Ornstein–Uhlenbeck Processes with Jumps in Hilbert Space. Potential Analysis 26:1, pages 79-100.
Crossref
V. Mandrekar & B. Rüdiger. 2008. Seminar on Stochastic Analysis, Random Fields and Applications V. Seminar on Stochastic Analysis, Random Fields and Applications V 261 274 .

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