Weak uniqueness for the heat equation with noise. (English) Zbl 0935.60045

Mytnik, Leonid

Ann. Probab. 26, No. 3, 968-984 (1998).

Summary: The uniqueness in law for the equation \(\partial X_t/ \partial t={1\over 2}\Delta X_t+ X^\gamma_t\dot W\) is established for \(1/2<\gamma<1\). The proof uses a duality technique and requires the construction of an approximating sequence of dual processes.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35R60	PDEs with randomness, stochastic partial differential equations

Keywords:

stochastic partial differential equation; martingale problem; duality

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