On the relation between the Itô and Stratonovich integrals in Hilbert spaces
Abstract
We examine the relation between the Itô and Stratonovich integrals in Hilbert spaces. A transition formula has origin in the correction term of the Wong-Zakai approximation theorem.
Keywords
stochastic integrals; Wong-Zakai approximations
References
2. R.F. Curtain, A.J. Pritchard, Infinite Dimensional Linear Systems Theory, Springer Verlag, Berlin 1978.
3. G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge 1991.
4. A.L. Dawidowicz, K. Twardowska, On the relation between the Stratonovich and ltô integrals with integrands of delayed argument, Demonstratio Math, XXVIII(2) (1995), 465-478.
5. H. Doss, Liens entre équations differentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré, XIII(2) (1977), 99-125.
6. D. Nualart, M. Zakai, On the relation between the Stratonovich and Ogawa integrals, Ann. Prob. 17(4) (1989), 1536-1540.
7. J.L. Solé, F. Utzet, Stratonovich integral and trace, Stochastics 29 (1980), 203-220.
8. R.L. Stratonovich, A new representation for stochastic integrals and equations, SIAM J. Control Optim. 4(2) (1966), 362-371.
9. K. Twardowska, An extension of Wong-Zakai theorem for stochastic evolution equations in Hilbert spaces, Stochastic Anal. Appl. 10(4) (1992), 471-500.
10. K. Twardowska, Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions, Dissertationes Math. 325 (1993), 1-54.
11. K. Twardowska, An approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations, Stochastic Anal. Appl. 13(5) (1995), 601-626.
12. K. Twardowska, An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations, Rend. Sem. Mat. Univ. Padova 96 (1996), 15-36.
Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska Poland
Katedra Matematyki, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
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