Given a weak solution of a semilinear stochastic partial differential equation, sufficient conditions for its uniqueness in law are presented. Moreover we characterize this law and prove that it is absolutely continuous with respect to the law of the process solving the corresponding linear stochastic partial differential equation, obtained neglecting the nonlinear term. The conditions imposed involve a P-a.s. assumption on the solution process. This allows to avoid a boundeness or linear growth condition on the nonlinear term. Finally, we prove the equivalence of the laws.
Uniqueness and absolute continuity for semilinear SPDE's
FERRARIO, BENEDETTA
2013-01-01
Abstract
Given a weak solution of a semilinear stochastic partial differential equation, sufficient conditions for its uniqueness in law are presented. Moreover we characterize this law and prove that it is absolutely continuous with respect to the law of the process solving the corresponding linear stochastic partial differential equation, obtained neglecting the nonlinear term. The conditions imposed involve a P-a.s. assumption on the solution process. This allows to avoid a boundeness or linear growth condition on the nonlinear term. Finally, we prove the equivalence of the laws.File in questo prodotto:
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