Asymptotic stability condition for stochastic Markovian systems of differential equations

We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the “original and the perturbated” control processes.

Averaging and stability of quasilinear functional differential equations with Markov parameters.

Katafygiotis, Lambros, Tsarkov, Yevgeny (1999)

Journal of Applied Mathematics and Stochastic Analysis

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Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations.

Shaikhet, Leonid E., Roberts, Jason A. (2006)

Advances in Difference Equations [electronic only]

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Stability of invariant sets of Itô stochastic differential equations with Markovian switching.

Luo, Jiaowan (2006)

Journal of Applied Mathematics and Stochastic Analysis

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