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Stochastic dynamics and passage times for diffusion approximations

Content Provider	Springer Nature Link
Author	Vittal, P. R. Jagadesan, T. Muralidhar, V.
Copyright Year	2008
Abstract	We discuss first passage time problems for a class of one dimensional master equations with separable kernels. For this class of master equations, the integral equations for first passage time moments (FPTM) have been transformed exactly into ordinary differential equations by Weiss and Szabo. There the boundary conditions for the first passage time moments have been introduced separately. In our study we use the imbedding method to derive the first passage time densities(FPTD) by imbedding the boundary conditions for crossing the barriers into the master equations. We also derived the results of Weiss and Szabo model from our results for first passage time densities and FPTM for crossing of the barriers. In our study we also derived the results the FPTD and FPTM by taking one of the barriers as absorbing and the other barrier as reflecting. When the separable kernel has only single term the equation for FPTD and FPTM obtained are exactly the same as that of simple diffusion. Generalisation of the model is studied to obtain the differential equations for FPTD and FPTM. The generalisation in the separable kernel leads to higher order differential equation for FPTD and FPTM. The differential equation for FPTM is identified with that of time homogeneous Fokker-Plank equation.
Starting Page	145
Ending Page	161
Page Count	17
File Format	PDF
ISSN	09713514
Journal	Differential Equations and Dynamical Systems
Volume Number	16
Issue Number	1-2
e-ISSN	09746870
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-05-16
Publisher Place	India
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Imbedding method Absorbing barrier Reflecting barrier Diffusion approximation Generalised separable kernel Stopping times; optimal stopping problems; gambling theory Optimal stopping Computer Science Engineering Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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