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The Stratonovich heat equation: a continuity result and weak approximations. (English) Zbl 1311.60067

The authors study the stochastic heat equation on the interval (0,1) driven by a trace-class Wiener process with multiplicative noise in Stratonovich form. They show existence and uniqueness of a mild solution and investigate convergence properties of various approximation schemes to the solution.
The reader interested in the topic of this paper may wish to also look at a more recent paper by M. Hairer and É. Pardoux [“A Wong-Zakai theorem for stochastic PDEs”, Preprint, arXiv:1409.3138] which treats essentially the same question for the corresponding Itō equation driven by space-time (and not just trace-class) noise using Hairer’s new theory of regularity structures.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
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