The renewal equation for persistent diffusion

V. Balakrishnan, S. Lakshmibala and C. Van Den Broeck

Physica A: Statistical Mechanics and its Applications, 1988, vol. 153, issue 1, 57-66

Abstract: Persistent diffusion in one dimension, in which the velocity of the diffusing particle is a dichotomic Markov process, is considered. The flow is non-Markovian, but the position and the velocity together constitute a Markovian diffusion process. We solve the coupled forward Kolmogorov equations and the coupled backward Kolmogorov equations with appropriate initial conditions, to establish a generalized (matrix) form of the renewal equation connecting the probability densities and first passage time distributions for persistent diffusion.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:153:y:1988:i:1:p:57-66

DOI: 10.1016/0378-4371(88)90101-X

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