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A singular perturbation approach to first passage times for Markov jump processes |
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| Authors: | C. Knessl B. J. Matkowsky Z. Schuss C. Tier |
| Affiliation: | (1) Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201 Evanston, Illinois;(2) Department of Mathematics, Tel Aviv University, Tel Aviv, Israel;(3) Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60680 Chicago, Illinois |
| Abstract: | We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods. |
| Keywords: | First passage time Markov jump process master equation singular perturbation asymptotic expansion |
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