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Asymptotic properties of jump-diffusion processes with state-dependent switching

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  • Xi, Fubao

Abstract

This work is concerned with a class of jump-diffusion processes with state-dependent switching. First, the existence and uniqueness of the solution of a system of stochastic integro-differential equations are obtained with the aid of successive construction methods. Next, the non-explosiveness is proved by truncation arguments. Then, the Feller continuity is established by means of introducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, the strong Feller continuity is proved by virtue of the relation between the transition probabilities of jump-diffusion processes and the corresponding diffusion processes. Finally, on the basis of the above results, the exponential ergodicity is obtained under the Foster-Lyapunov drift conditions. Some examples are provided for illustration.

Suggested Citation

  • Xi, Fubao, 2009. "Asymptotic properties of jump-diffusion processes with state-dependent switching," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2198-2221, July.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:7:p:2198-2221
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    References listed on IDEAS

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    1. Wee, In-Suk, 1999. "Stability for multidimensional jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 193-209, April.
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    5. Wu, Liming, 2001. "Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 205-238, February.
    6. Xi, Fubao, 2004. "Stability of a random diffusion with nonlinear drift," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 273-286, July.
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    Cited by:

    1. Chen, Xingzhi & Xu, Xin & Tian, Baodan & Li, Dong & Yang, Dan, 2022. "Dynamics of a stochastic delayed chemostat model with nutrient storage and Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Xi, Fubao & Yin, George, 2013. "The strong Feller property of switching jump-diffusion processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 761-767.
    3. Min Qian & Fuxi Zhang, 2011. "Entropy Production Rate of the Coupled Diffusion Process," Journal of Theoretical Probability, Springer, vol. 24(3), pages 729-745, September.
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    5. Xi, Fubao & Zhu, Chao, 2018. "On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4277-4308.

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