Asymptotic Properties of Parabolic Systems for Null-Recurrent Switching Diffusions  

作　　者：R.Z.Khasminskii 

机构地区：[1]Department of Mathematics Wayne State University Detroit MI 48202 USA.

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第2期177-194,共18页应用数学学报（英文版）

基　　金：the National Science Foundation under DMS-0603287;the National Security Agency,MSPF-068-029; the National Natural Science Foundation of China under No.60574069

摘　　要：This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A sufficient condition for null recurrence is presented. Moreover, convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established. Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain. To verify the condition, boundary value problems （BVPs） for parabolic systems are treated, which are not the usual two-point BVP type. An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A sufficient condition for null recurrence is presented. Moreover, convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established. Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain. To verify the condition, boundary value problems （BVPs） for parabolic systems are treated, which are not the usual two-point BVP type. An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.

关 键 词：Parabolic system switching diffusion null recurrence Markov chain 

分 类 号：O211.62[理学—概率论与数理统计]