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 suffi...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.展开更多
基金the National Science Foundation under DMS-0603287the National Security Agency,MSPF-068-029 the National Natural Science Foundation of China under No.60574069
文摘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.
