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
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One o...This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.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.
基金in part by the National Science Foundation under grant DMS-9971608in part by the Office of Naval Research under grant N00014-95-1-0793+1 种基金in part by the National Science Foundation under grant DMS-9971608in part by the National Science Foundation
文摘This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
