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Original Articles

Remarks on the existence and approximation for semilinear stochastic differential equations in Hilbert spaces

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Pages 495-518 | Published online: 15 Feb 2007

REFERENCES

  • Bahlali , K. , Mezerdi , B. and Ouknine , Y. 1998 . “ Pathwise Uniqueness and Approximation of Solutions of Stochastic Differential Applications ” . In Séminaire de Probabilité XXXII 166 – 187 . Berlin : Springer Verlag .
  • in press .
  • Bensoussan , A. , Glowinski , R. and Rascanu , A. 1992 . Approximation of Some Stochastic Differential Equations by the Splitting Method . Appl. Math. Optim. , 25 : 81 – 106 .
  • Bihari , I. 1965 . A Generalisation of Lemma of Bellman and its Applications to Uniqueness Problem of Differential Equations . Acta Math. Acad. Sci. Hung. , 7 : 71 – 94 .
  • Coddington , E.A. and Levinson , N. 1955 . Theory of Ordinary Differential Equations New York : McGraw-Hill .
  • Chojnowska-Michalik , A. 1979 . “ Stochastic Differential Equations in Hilbert Spaces ” . In Probability Theory Vol. 5 , 53 – 74 . PWN, Warszawa : Banach Center Publications .
  • Da Prato , G. , Kwapien , S. and Zabczyk , J. 1987 . Regularity of Solutions of Linear Stochastic Equations in Hilbert Spaces . Stochastics , 23 : 1 – 23 .
  • Da Prato , G. and Zabczyk , J. 1992 . Stochastic Equations in Infinite Dimensions New York : Cambridge University Press .
  • Da Prato , G. and Zabczyk , J. 1996 . Ergodicity for Infinite Dimensional Systems New York : Cambridge University Press .
  • Erraoui , M. and Ouknine , Y. 1994 . Sur la Convergence de la Formule de Lie-Trotter pour les Équations Differentielles Stochastiques . Ann. Math. Blaise Pascal , 1 ( 2 ) : 7 – 13 .
  • Erraoui , M. and Ouknine , Y. 1994 . Approximations des Équations Differentielles Stochastiques par des Équations à Retard . Stoch. Stoch. Rep. , 46 : 53 – 62 .
  • Erraoui , M. and Eddahbi , M. in press . On Quasi-linear Parabolic SPDEs with Non Lipschitz Coefficients . Random Operators Stoch. Equations ,
  • in press .
  • Gatarek , D. and Goldys , B. 1994 . On Weak Solutions of Stochastic Equations in Hilbert Spaces . Stoch. Stoch. Rep. , 46 : 41 – 51 .
  • Goldys , B. 1992 . On Weak Solutions of Stochastic Evolutions Equations with Unbounded Coefficients. Miniconference on probability and analysis (Sydney 1991) . Proc. Centre Math. Appl. Aust. Nat. Univ., Aust. Nat. Univ., Canberra , 29
  • Gyöngy , I. and Krylov , N. 1996 . Existence of Strong Solutions for Itô's Stochastic Equations via Approximations . Probab. Theory Relat. Fields , 105 : 143 – 158 .
  • in press .
  • Ichikawa , A. 1982 . Stability of Semilinear Stochastic Evolution Equations . J. Math. Anal. Appl. , 90 : 12 – 44 .
  • Kaneko , H. and Nakao , S. 1988 . “ A Note on Approximation for Stochastic Differential Equations ” . In Séminaire de Probabilité XII Edited by: Azéma , J. , Meyer , P.A. and Yor , M. 155 – 165 . Berlin : Springer-Verlag .
  • Kozlov , S.M. 1978 . Some Questions Concerning Stochastic Differential Equations with Partial Derivatives . Trudy Seminara Petrovskogo , 4 : 147 – 172 . (in Russian)
  • Leha , G. and Ritter , G. 1994 . Lyapunov-Type Conditions for Stationary Distributions of Diffusion Processes on Hilbert Space . Stoch. Stoch. Rep. , 48 : 195 – 225 .
  • Leha , G. , Ritter , G. and Wakolbinger , A. 1997 . An Improved Lyapunov-Function Approach to the Behavior of Diffusion Process in Hilbert Spaces . Stoch. Anal. Appl. , 15 : 59 – 89 .
  • Liu , K. 1998 . On Approximate Solution of Stochastic Delay Evolution Equation in Infinite Dimensions . Numer. Funct. Anal. Optim. , 19 ( 1–2 ) : 81 – 90 .
  • Métivier , M. 1988 . Stochastic Partial Differential Equations in Infinite Dimensional Spaces Pisa : Scuola Normale Superiore di Pisa .
  • Rodkina , A.E. 1984 . “ On Existence and Uniqueness of Solution of Stochastic Differential Equations with Heredity ” . In Stochastics Monographs Vol. 12 , 187 – 200 . New York : Gordon and Breach .
  • Seidler , J. 1997 . Weak Convergence of Infinite-Dimensional Diffusions . Stoch. Anal. Appl. , 15 : 399 – 417 .
  • Taniguchi , T. 1992 . Successive Approximations to Solutions of Stochastic Differential Equations . J. Differ. Equations , 96 : 152 – 169 .
  • Tudor , C. 1984 . Successive Approximations for Solutions of Stochastic Integral Equations of Volterra Type . J. Math. Anal. Appl. , 104 : 27 – 37 .
  • Viot , M. “ Solutions Faibles d'Equations aux Dérivées Partielles non Linéaires ” . Université Paris VI .
  • Yamada , T. 1981 . On the Successive Approximation of Solutions of Stochastic Differential Equations . J. Math. Kyoto Univ. , 21 : 501 – 515 .

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