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Stability of a random diffusion with nonlinear drift

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  • Xi, Fubao
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    Abstract

    For the solution to a rather general nonlinear stochastic differential equation with Markovian switching, we first prove its Feller continuity and the existence and uniqueness of invariant measure by the coupling method, then discuss its stability in total variation norm by the Foster-Lyapunov inequality.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4CG7NN7-1/2/72dcba39eca88321275f1c817dd74c24
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 3 (July)
    Pages: 273-286

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    Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:273-286

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    Related research

    Keywords: Coupling Feller continuity Stability Total variation Foster-Lyapunov inequality;

    References

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    1. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:
    1. Xi, Fubao & Yin, G., 2010. "Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1378-1389, July.
    2. Xi, Fubao, 2009. "Asymptotic properties of jump-diffusion processes with state-dependent switching," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(7), pages 2198-2221, July.

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