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Stability in distribution of neutral stochastic differential delay equations with Markovian switching. (English) Zbl 1175.34103

Summary: We focus on stochastic delay differential equations in the form: for τ>0

d[x(t)-G(x(t-τ))]=f(x(t),x(t-τ),r(t))dt+g(x(t),x(t-τ),r(t))dB(t),t0,(2·1)

We are concerned with neutral stochastic differential delay equations with Markovian switching (NSDDEwMSs). We derive sufficient conditions for stability in distribution and generalize some results of Basak et al. and Yuan et al. to cover a class of much more general NSDDEwMSs. In the end, two examples are established to demonstrate the theory of our work.

MSC:
34K50Stochastic functional-differential equations
60H10Stochastic ordinary differential equations
34K20Stability theory of functional-differential equations
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