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Variational formula for the stability of regime-switching diffusion processes. (English) Zbl 1391.60185

Summary: The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coeffcients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
93E15 Stochastic stability in control theory
60A10 Probabilistic measure theory
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