Abstract and Applied Analysis

Feller Property for a Special Hybrid Jump-Diffusion Model

Jinying Tong

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Abstract

We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 412848, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606748

Digital Object Identifier
doi:10.1155/2014/412848

Mathematical Reviews number (MathSciNet)
MR3200783

Citation

Tong, Jinying. Feller Property for a Special Hybrid Jump-Diffusion Model. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 412848, 8 pages. doi:10.1155/2014/412848. https://projecteuclid.org/euclid.aaa/1412606748


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References

  • X. R. Mao, “Stability of stochastic differential equations with Markovian switching,” Stochastic Processes and Their Applications, vol. 79, no. 1, pp. 45–67, 1999.
  • L. Shaikhet, “Stability of stochastic hereditary systems with Markov switching,” Theory of Stochastic Processes, vol. 2, no. 18, pp. 180–184, 1996.
  • X. R. Mao, A. Matasov, and A. B. Piunovskiy, “Stochastic differential delay equations with Markovian switching,” Bernoulli, vol. 6, no. 1, pp. 73–90, 2000.
  • I.-S. Wee, “Stability for multidimensional jump-diffusion processes,” Stochastic Processes and Their Applications, vol. 80, no. 2, pp. 193–209, 1999.
  • C. G. Yuan and X. R. Mao, “Asymptotic stability in distribution of stochastic differential equations with Markovian switching,” Stochastic Processes and Their Applications, vol. 103, no. 2, pp. 277–291, 2003.
  • Z. Z. Zhang and D. Y. Chen, “A new criterion on existence and uniqueness of stationary distribution for diffusion processes,” Advances in Difference Equations, vol. 13, pp. 1–6, 2013.
  • F. B. Xi, “Stability of a random diffusion with nonlinear drift,” Statistics & Probability Letters, vol. 68, no. 3, pp. 273–286, 2004.
  • F. B. Xi, “On the stability of jump-diffusions with Markovian switching,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 588–600, 2008.
  • M. F. Neuts, “Computational uses of the method of phases in the theory in the theory of queues,” Computers & Mathematics with Applications, vol. 1, pp. 151–166, 1975.
  • N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, The Netherlands, 1989.
  • M. F. Chen and S. F. Li, “Coupling methods for multidimensional diffusion processes,” The Annals of Probability, vol. 17, no. 1, pp. 151–177, 1989.
  • M.-F. Chen, From Markov Chains to Non-Equilibrium Particle Systems, World Scientific, Singapore, 2004.
  • A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, American Mathematical Society, Providence, RI, USA, 1989. \endinput