The moment and almost surely exponential stability of stochastic heat equations

Xie, Bin

doi:10.1090/S0002-9939-08-09458-6

The moment and almost surely exponential stability of stochastic heat equations
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Proc. Amer. Math. Soc. 136 (2008), 3627-3634 Request permission

Abstract:

In this article, the $p$-th moment and almost surely exponential stability of the strong solution to a stochastic heat equation driven by an $m$-dimensional Brownian motion is investigated by a simple method. In particular, the sharp top Lyapunov exponents are explicitly calculated based on the representation of the strong solution.

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