Chapter 8. Invariant Measures and Asymptotic Behavior of Stochastic Evolution Equations
Oleksandr Misiats1, Oleksandr Stanzhytskyi2, Viktoriia Mogylova3 and Ihor Korol4,5
1Virginia Commonwealth University, Richmond, VA, US
2Taras Shevchenko National University of Kyiv, Ukraine
3Igor Sirkorsky National Polytechnic University of Kyiv, Ukraine
4The John Paul II Catholic University of Lublin, Poland
5Uzhhorod National University, Ukraine
Part of the book: Stochastic Processes: Fundamentals and Emerging Applications
This work is devoted to investigation of large time asymptotic behavior of stochastic partial differential equations (SPDEs). This problem is closely related to the problem of existence and uniqueness of stationary solutions and invariant measures, which in certain cases possess attractive properties. We obtain the sufficient conditions for the existence and uniqueness of invariant measures for a large class of SPDEs of reaction-diffusion type.
Keywords: invariant measure, stationary solution, dissipation condition, monotonicity condition, stochastic homogenization, non-Lipschitz coefficients
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