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Lyapunov exponents of hybrid stochastic heat equations. (English) Zbl 1250.93122
Summary: In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the \(p\)-th moment Lyapunov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by Markovian switching.

93E15 Stochastic stability in control theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J75 Jump processes (MSC2010)
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