Strong Uniqueness for an SPDE via backward doubly stochastic differential equations
نویسندگان
چکیده
We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward doubly stochastic differential equations, when used with the Yamada-Watanabe method, gives a short proof of strong uniqueness.
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