Strong uniqueness for an SPDE via backward doubly stochastic differential equations

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t,x) and its derivative ∂xv(t,x). The familiar Yamada-Watanabe 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.