93
Views
25
CrossRef citations to date
0
Altmetric
Original Articles

An approximation theorem of wong-zakai type for nonlinear stochastic partial differential equations

Pages 601-626 | Published online: 03 Apr 2007

References

  • Aquistapace , J.P. and Terreni , B. 1984 . An approach to Ito linear equations in Hilbert spaces by approximation of white noise with coloured noise . Stochastic Anal. Appl , 2 : 131 – 186 .
  • Bensoussan , A. 1992 . Some existence results for stochastic partial differential equations . pitman Research Notes in Math , 268 : 37 – 53 .
  • Bensoussan , A. and Temam , R. 1972 . Equations aux dérivés partielles stochastiques nonlineairés . Isr. J. Math , 11 ( 1 ) : 95 – 129 .
  • Brzéniak , Z. , Capiński , M. and Flandoli , F. 1988 . A convergence result for stochastic partial differential equations . Stochastics , 24 ( 1 ) : 423 – 445 .
  • Curtain. , R.F. and Pritchard , A.J. 1978 . Infinite Dimensional Linear System Theory , Berlin : Springer .
  • Dawson , D.A. 1975 . Stochastic evolution equations and related measure process . J. Mult. Anal , 5 : 1 – 52 .
  • Doss , H. 1977 . Liens entre equations differentielles stochastiques et ordinaries . Ann. Inst.H. Poincaré , 13 ( 2 ) : 99 – 125 .
  • Fleming , W. 1975 . “ Distributed parameter stochastic systems in population biology ” . In Int. Symp. IRIA , 179 – 191 . Berlin : Springer . Lecture Notes in Econ. and Math. Syst. 107
  • Gyöngy , I. 1982 . On stochastic equations with respect to semimartinagales III . Stochastics , 7 : 231 – 254 .
  • Gyöngy , I. 1989 . “ The stability of stochastic differential equations and applications ” . In Theorems on supports , 91 – 118 . Berlin : Springer . in:Lecture Notes in Math. 1390
  • Ikeda , N. and Watanabe , S. 1981 . Stochastic Differential Equations and Diffusion Processes , Amsterdam : North-Holland .
  • Krylov , N.U. and Rozovskii , B.L. 1979 . “ On stochastic evolution equations ” . In Itogi Nauki i Techniki , Vol. 14 , 71 – 146 . Moscow, , Russia : Teor.Verojatn .
  • Lions , J.L. 1969 . Quelques Méthodes de Résolution de Problèmes aux Limites non Linéaires , Paris : Dunod .
  • Mackevičius , W. 1986 . On the support of a solution of vochastic differential equation . Lietuvos Matematikos Rinkinys , 26 ( 1 ) : 91 – 98 .
  • Metivier , M. and Pistone , G. 1975 . Une formule d’iso métrie pour l’intégrale stochastique hilbertienneet équations d’evolution linéaires stochastiques . z.Wahrscheinlichkeitstheorie und Verw. Geb , 33 ( 1 ) : 1 – 18 .
  • Nakao , S. and Yamato , Y. . Approximation theorem of stochastic differential equations . Proc.Internat.Sympos. SDE . 1976 , Kyoto. pp. 283 – 196 . Tokyo
  • Pardoux , E. 1975 . “ Equations aux dédérivées partielles stochastiques non linéaires monotones ” . In Etude de solutions fortes de type Itô , Paris : Thése Doct. Sci. Math. Univ .
  • Pardoux , E. 1979 . Stochastic partial differential equations and filtering of diffusion processes . Stochastics , 3 : 127 – 137 .
  • Rozovskii , B.L. 1990 . “ Stochastic Evolution Systems ” . In Linear Theory and Applications to Non- linear Filtering , Dordrecht : Kluwer .
  • Tanabe , H. 1979 . “ Equations of Evolution ” . In Monographs andStudies in Math Vol. 6 , Pitman, London
  • Twardowska , K. 1992 . An extension of the Wong-Zakai theorem for stochastic evolution equations in Hilbert spaces . Stochastic Anal. Appl , 10 : 471 – 500 .
  • Twardowska , K. 1993 . Approximation theorems Zakai type for stochastic differential in infinite dimensions . Dissertationes Math , 325 : 1 – 54 .
  • Wong , E. and Zakai , M. 1965 . On the convergence of ordinary integrals to stochastic integrals . Ann.Math. statist , 36 : 1560 – 1564 .

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:

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:

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.