JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NOTE ON EXPONENTIAL ALMOST SURE STABILITY OF STOCHASTIC DIFFERENTIAL EQUATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NOTE ON EXPONENTIAL ALMOST SURE STABILITY OF STOCHASTIC DIFFERENTIAL EQUATION
Mao, Xuerong; Song, Qingshuo; Yang, Dichuan;
  PDF(new window)
 Abstract
Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.
 Keywords
almost sure stability;stochastic differential equation;regime-switching;Besel squared process;
 Language
English
 Cited by
 References
1.
R. Z. Has'minskii, Stochastic Stability of Differential Equations, Volume 7 of Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980.

2.
I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, Volume 39 of Applications of Mathematics (New York), Springer-Verlag, New York, 1998.

3.
X. Mao, Stochastic Differential Equations and Their Applications, Horwood Publishing Series in Mathematics & Applications. Horwood Publishing Limited, Chichester, 1997.

4.
X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, London, 2006.

5.
M. Metivier, Semimartingales, Volume 2 of de Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin, 1982.

6.
D. Revuz and M. Yor, Continuous Martingales And Brownian Motion, Third edition, Springer-Verlag, Berlin, 1999.

7.
J. A. Yan, Yang yu suiji jifen yinlun, Shanghai Science and Technology Publishing House, Shanghai, 1981.

8.
G. G. Yin and Q. Zhang, Continuous-time Markov chains and applications, Volume 37 of Applications of Mathematics (New York), Springer-Verlag, New York, 1998.

9.
G. G. Yin and C. Zhu, Hybrid switching diffusions, Properties and applications, Volume 63 of Applications of Mathematics (New York), Springer-Verlag, New York, 2010.

10.
C. Yuan and X. Mao, Robust stability and controllability of stochastic differential delay equations with Markovian switching, Automatica J. IFAC 40 (2004), no. 3, 343-354. crossref(new window)