Abstract. We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in Rn of the Klein—Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied.
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Barbu, ., Prato, . The Stochastic Nonlinear Damped Wave Equation . Appl Math Optim 46, 125–141 (2002). https://doi.org/10.1007/s00245-002-0744-4
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DOI: https://doi.org/10.1007/s00245-002-0744-4