Electron. J. Diff. Eqns., Vol. 2004(2004), No. 05, pp. 1-30.

Periodic and invariant measures for stochastic wave equations

Jong Uhn Kim

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.

Submitted December 15, 2002. Published January 2, 2004.
Math Subject Classifications: 35L65, 35R60, 60H15.
Key Words: Wave equation, Brownian motion, periodic measure, invariant measure, probability distribution, tightness.

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Jong Uhn Kim
Department of Mathematics, Virginia Tech
Blacksburg, VA 24061-0123, USA
email: kim@math.vt.edu

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