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On the stability of jump-diffusions with Markovian switching. (English) Zbl 1138.60044

Under the standard Lipschitz condition and linear growth condition of coefficients, the existence, uniqueness and non-explosion of solutions to a class of stochastic differential-integral equations driven by the Brownian motion and the Poisson process with Markovian switching are proved. Feller and strong Feller properties and the exponential ergodicity for the associated Markov semigroups are also investigated.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
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