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Periodic and invariant measures for stochastic wave equations

Keywords: Wave equation , Brownian motion , periodic measure , invariant measure , probability distribution , tightness.

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Abstract:

We establish the existence of periodic and invariant measures for a semilinear wave equation with random noise. These are counterparts of time-periodic and stationary solutions of a deterministic equation. The key element in our analysis is to prove that the family of probability distributions of a solution is tight.

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