对称Levy乘性噪声下平均首次逃逸时问题的计算分析
A Computational Analysis for First Mean Exit Time under Symmetrical Levy Multiplicative Noise
摘要:
复杂的动力系统常常受到非高斯的随机扰动。首次逃离现象,即从一个状态空间的有界区域中逃逸出来,对动力系统的随机演化有很大的影响。在本文中,我通过计算分析了在乘性Levy噪声下的首次逃离时问题。一个数值的方法去求解这个非局部的问题,计算分析出不同的跳测度系数和值对系统的首次逃离时间的影响。
>Complex dynamical systems are often subject to non-Gaussian random fluctuations. The exit phe- nomenon, i.e., escaping from a bounded domain in state space, has a great impact on the stochastic evolution of such dynamical systems. In the present paper, the author analyzes mean exit time for arbitrary noise inten- sity under multiplicative noise, via numerical investigation. A numerical approach for solving this non-local problem is proposed. A computational analysis is conducted to investigate the relative importance of jump measure coefficient and the effect of value on first exit time.
参考文献
[1]
|
Chen, H., Duan, J., Li, X., et al. (2011) A computational analysis for mean exit time under non-Gaussian Levy noises. Applied Mathematics and Computation, 218, 1845-1856.
|
[2]
|
Peszat, S. and Zabczyk, J. (2007) Stochastic partial differential equations with levy processes. Cambridge University Press, Cambridge.
|
[3]
|
Applebaum, D. (2004) Levy processes and stochastic calculus. Cambridge University Press, Cambridge.
|
[4]
|
Peszat, S. and Zabczyk, J. (2007) Stochastic partial differential equations with levy processes. Cambridge University Press, Cambridge.
|
[5]
|
Sato, K.I. (1999) Levy processes and infinitely divisible distributions. Cambridge University Press, Cambridge.
|
[6]
|
Getoor, R.K. (1961) First passage times for symmetric stable processes in space. Transactions of the American Mathematical Society, 101, 75- 90.
|
[7]
|
Oksendal, B. (2005) Applied stochastic control of jump diffusions. Springer-Verlag, New York.
|
[8]
|
Schuss, Z. (1980) Theory and applications of stochastic differential equations. Wiley &Sons, New York.
|
[9]
|
Naeh, T., Klosek, M.M., Matkowsky, B.J., et al. (1990) A direct approach to the exit problem. SIAM Journal on Applied Mathematics, 50, 595-627.
|
[10]
|
Apostol, T.M. (1974) Mathematical analysis. 2nd Edition, Addison-Wesley, Boston.
|