Abstract
By solving a deterministic Skorohod problem in the framework of evolutional triple, we prove the existence and uniqueness of solutions to multivalued stochastic evolution equations involving maximal monotone operators. The existence and uniqueness of invariant measures associated with the solutions as Markov processes are also considered in the present paper. Moreover, we apply the results to stochastic differential equations with normal reflecting boundary conditions and with singular drift terms, as well as a class of multivalued nonlinear stochastic partial differential equations with possibly discontinuous coefficients.
| Original language | English |
|---|---|
| Pages (from-to) | 175-217 |
| Number of pages | 43 |
| Journal | Bulletin des Sciences Mathematiques |
| Volume | 131 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Mar 2007 |
| Externally published | Yes |
Keywords
- Evolutional triple
- Invariant measure
- Maximal monotone operator
- Multivalued stochastic equation
- Skorohod problem
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Zhang, X. (2007). Skorohod problem and multivalued stochastic evolution equations in Banach spaces. Bulletin des Sciences Mathematiques, 131(2), 175-217. https://doi.org/10.1016/j.bulsci.2006.05.009