An approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations. (English) Zbl 0839.60059
Summary: We present an extension of the Wong-Zakai approximation theorem for nonlinear stochastic partial differential equations defined in abstract spaces and with some Hilbert space valued disturbances given by the Wiener process and a martingale. By approximating these disturbances we obtain in the limit equation the Itô correction term for the infinite-dimensional case. Such form of the correction term connected with the Wiener process was proved in the author’s papers [ibid. 10, No. 4, 471-500 (1992; Zbl 0754.60060) and Diss. Math. 325 (1993; Zbl 0777.60051)], where the approximation theorem for semilinear stochastic evolution equations in Hilbert spaces was studied. Our model here is similar as the one considered by E. Pardoux [“Equations aux dérivées partielles stochastiques non linéaires monotones. Etude de solutions fortes de type Itô” (Thèse, Univ. Paris Sud, 1975)].
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60F15 | Strong limit theorems |
References:
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