Skorohod problem and multivalued stochastic evolution equations in Banach spaces
The author proves existence and uniqueness of solutions to multi-valued stochastic evolution equations involving maximal monotone operators. For this purpose, a deterministic Skorohod problem in the framework of evolutional triple is solved. The existence and uniqueness of invariant measures associated with the solutions as Markov processes are also considered. Moreover, the author applies the results to stochastic differential equations with normal reflecting boundary conditions and with singular drift terms, as well as to a class of multi-valued nonlinear stochastic partial differential equations with possibly discontinuous coefficients.
stochastic partial differential equations
scientific article; zbMATH DE number 5134236
scientific article