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

Fubao Xi

Stochastic Processes and their Applications, 2009, vol. 119, issue 7, 2198-2221

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.

Keywords: Jump; diffusion; State-dependent; switching; Feller; continuity; Auxiliary; process; Radon-Nikodym; derivative; Strong; Feller; continuity; Exponential; ergodicity (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (5)

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