On stochastic convolution in banach spaces and applications

References

• Agmon , S. , Douglis , A. and Nirenberg , L. 1959 . Estimates near boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I . Comm. Pure Appl. Math , 12 : 623 – 727 .
   Google Scholar
• Agmon , S. , Douglis , A. and Nirenberg , L. 1964 . Estimates near boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II . Comm. Pure Appl. Math , 17 : 35 – 92 .
   Google Scholar
• Baxendale , P. 1976 . Gaussian measures on Function Spaces . Amer. J. Math , 98 : 891 – 952 .
   Google Scholar
• Beauzamy , B. 1985 . “ Introduction to Banach Spaces and their Geometry ” . In Mathematical Studies , Vol. 68 , Amsterdam : North Holland .
   Google Scholar
• Belopolskaya , Ya. , Dalecky , L. and Yu. , L. 1990 . “ Stochastic Equations and Differential Geometry ” . In Mathematics and Its Applications , Vol. 30 , Dortrecht Boston London : Kluwer Academic Publishers .
   Google Scholar
• Bergh , J. and Löfström , J. 1976 . “ Interpolation Spaces ” . Berlin Heidelberg New York : Springer-Verlag .
   Google Scholar
• Brzeźniak , Z. 1991 . “ Stochastic Partial Differential Equations in M-type 2 Banach spaces and Stochastic Partial Differential Equations in M type 2 Banach spaces ” . In BIBoS Vol. II , Preprints
   Google Scholar
• Brzeźniak , Z. 1995 . Stochastic Partial Differential Equations in M-type 2 Banach spaces . Potential Analysis , 4 : 1 – 45 .
   Google Scholar
• Brzeźniak , Z. 1996 . “ On Sobolev and Besov spaces regularity of Brownian paths ” . In Stochastics and Stochastics Reports Vol. 56 , 1 – 15 .
   Google Scholar
• Brzeźniak , Z. and Elworthy , D. Stochastic Flows of Diffeomorphisms for Stochastic Differential Equations, functional analytic approach . Proceedings of the Fifth Gregynog Stochastic Analysis Symposium “Stochastic Analysis and Applications” . Gregynog, Wales (1995). Edited by: Davies , I. M. , Truman , A. and Elworthy , K. D. pp. 107 – 138 . Singapore : World Scientific .
   Google Scholar
• Brzeźniak , Z. and Elworthy , D. 1996 . “ Stochastic differential equations on Banach manifolds; applications to diffusions on loop spaces ” . Warwick . Preprint
   Google Scholar
• Brzeźniak , Z. and Gatarek , D. 1996 . “ Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces ” . Hull Preprint
   Google Scholar
• Brzeźniak , Z. and Peszat , S. in peparation
   Google Scholar
• Burkholder , D. L. 1986 . “ Martingales and Fourier Analysis in Banach Spaces ” . In Probability and Analysis (Varenna 1985), LNM , Vol. 1206 , 61 – 108 . Berlin Heidelberg New York : Springer Verlag .
   Google Scholar
• Chojnowska-Michalik , A. 1977 . “ Stochastic differential equations in Hilbert spaces and some of their applications ” . In Thesis, Institute of Mathematics , Polish Academy of Sciences .
   Google Scholar
• Chow , P.-L. and Jiang , J.-J. 1994 . Stochastic partial differential equations in Hölder spaces . Probab. Theory Relat. Fields , 99 : 1 – 27 .
   Google Scholar
• Curtain , R. F. and Falb , P. 1971 . Stochastic differential equations in Hilbert spaces . J. Diff. Equat , 10 : 412 – 430 .
   Google Scholar
• Da Prato , G. 1983 . Some results on linear stochastic evolution equations in Hilbert spaces by the semigroup method . Stoch. Anal. Appl , 1 : 57 – 88 .
   Google Scholar
• Da Prato , G. , Kwapień , S. and Zabczyk , J. 1987 . Regularity of Solutions of linear Stochastic Equations in Hilbert spaces . Stochastics , 23 : 1 – 23 .
   Google Scholar
• Da Prato , G. and Zabczyk , J. 1992 . “ Stochastic Equations in Infinite Dimensions ” . In Encyclopedia of Mathematics and Its Applications , Vol. 44 , Cambridge : Cambridge University Press .
   Google Scholar
• Dawson , D. A. 1975 . Stochastic evolution equations and related measure processes . J. Multivar. Anal , 5(1) : 1 – 52 .
   Google Scholar
• Dettweiler , E. 1991 . Stochastic Integration Relative to Brownian Motion on a General . Doğa – Tr. J. of Mathematics , 15 : 6 – 44 .
   Google Scholar
• Donati-Martin , C. and Paradoux , E. 1993 . White noise driven SPDEs with reflection . Prohab. Theory Relat. Fields , 95 : 1 – 24 .
   Google Scholar
• Dore , G. and Venni , A. 1987 . On the Closcdness of the Sun of Two Closed Operators . Math. J , 196 : 189 – 201 .
   Google Scholar
• Elworthy , D. 1982 . “ Stochastic Differential Equations on Manifolds ” . In Math. Soc , Vol. LNS 70 , London : Cambridge University Press .
   Google Scholar
• Flandoli , F. 1991 . “ A stochastic reaction-diffusion equation with multiplecative noise ” . In Appl. Math. Letters Vol. 4 , 45 – 48 .
   Google Scholar
• Flandoli , F. 1992 . On the semigroup approach to Stochastic Evolution Equations . Stochastic Analysis and Applications , 10(2) : 181 – 203 .
   Google Scholar
• Giga , Y. and Sohr , H. 1991 . Abstract Lp Estimates for the Cauchy Problem with Applications to the Navier-Stokes Equations in Exterior Domains . J. Fund. Anal , 102 : 72 – 94 .
   Google Scholar
• Henry , D. 1981 . “ Geometric Theory of Semilinear Parabolic Equations ” . In Lecture Notes in Mathematics , Berlin Heidelberg New York : Springer Verlag .
   Google Scholar
• Ichikawa . 1984 . Semilinear stochastic evolution equations: Boundedness, stability and invariant measures . Stochastics , 12 : 1 – 39 .
   Google Scholar
• Krylov , N. and Rozovskii , B. L. 1979 . Stochastic Evolution Equations, Itogi Naukii Tekhniki . Seria Sovremiennyie Prohlemy Matematiki , 14 : 71 – 146 . (in Russian)
   Google Scholar
• Kunita , H. 1990 . “ Stochastic Flows and Stochastic Differential Equations ” . Cambridge University Press .
   Google Scholar
• Kuo , H. H. 1975 . “ Gaussian Measures in Banach Spaces ” . In Lect. Notes Maths , Berlin : Springer Verlag .
   Google Scholar
• Lions , J. L. 1969 . “ Quelques Methodes de Résolution des Problèmes Aux Limites Non Linéaires ” . Paris : Dunod .
   Google Scholar
• Malliavin , P. 1986 . “ Stochastic Differential Equations and Cylindrical Vector Valued Martingales ” . In Aspects of Mathematics and its Applications , Edited by: Barosso , J. A. 583 – 599 . B.V : Elsevier Science Publishers .
   Google Scholar
• Neidhardt , A. L. 1978 . “ Stochastic Integrals in 2-uniformly smooth Banach Spaces, University of Wisconsin ” .
   Google Scholar
• Pardoux , E. 1975 . “ Equations aux derivees partielles stochastiques non lineaires monotones ” . In These Paris XL
   Google Scholar
• Pardoux , E. 1979 . Stochastic Partial Differential Equations and Filtering of Diffusion Processes . Stochastics , 3 : 127 – 167 .
   Google Scholar
• Pazy , A. 1983 . “ Semigroups of Linear Operators and Applications to Partial Differential Equations ” . In Applied Mathematical Sciences , Berlin Heidelberg New York : Springer-Verlag .
   Google Scholar
• Peszat , S. 1995 . Existence and uniqueness of the solution for stochastic equations on Banach spaces . Stochastics and Stochastics Rep , 55 : 167 – 193 .
   Google Scholar
• Pisier , G. 1976 . Martingales with values in uniformly convex spaces . Israel Journal of Mathematics , 20 : 326 – 350 .
   Google Scholar
• Pisier , G. 1986 . “ Probabilistic Methods in the Geometry of Banach Spaces ” . In Probability and Analysis (Varenna 1985), LNM , Vol. 1206 , 167 – 241 . Berlin Heidelberg New York : Springer Verlag .
   Google Scholar
• Prüss , J. and Sohr , H. 1990 . On Operators with Bounded Imaginary Powers . Math. Z , 203 : 429 – 452 .
   Google Scholar
• Schwartz , L. 1967 . “ Analyse Mathématique ” . In Cows professé à I'Ecole Poly technique, Paris , Paris : Hermann .
   Google Scholar
• Seidler , J. 1993 . Da-Prato-Zabczyk's maximal inequality revisited I . Math.Bohem , 118 : 67 – 106 .
   Google Scholar
• Temam , R. 1982 . Behaviour at time t= 0 of the solutions of semilinear evolution equations . J. Differential Equations , 43 : 73 – 92 .
   Google Scholar
• Triebel , H. 1978 . “ Interpolation Theory, Function Spaces ” . In Differential Operators , Amsterdam New York Oxford : North-Holland .
   Google Scholar
• Vakhania , N. N. , Tarieladze , V. I. and Chobanyan , S. A. 1987 . “ Probability Distributions on Banach Spaces ” . Dortrecht : Reidel .
   Google Scholar
• Walsh , J. B. 1986 . “ An introduction to stochastic partial differential equations ” . In Ecole d'été de Probabilités de Saint Flour, LNM , Edited by: Hennequin , P. L. Vol. 1180 , 265 – 437 . Berlin Heidelberg New York : Springer Verlag .
   Google Scholar