A new stochastic description of random jump processes with memory: the overall jump rate as a random variable

A new stochastic description of random jump processes with memory is suggested. The method is based on the assumption that the overall jump rate is a supplementary random state variable. We assume that the joint probability for the jump rate as well as for other state variables fulfills a Markovian...

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Bibliographic Details
Published inPhysics letters. A Vol. 158; no. 3; pp. 149 - 152
Main Authors Ovidiu Vlad, M., Kehr, K.W.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 26.08.1991
Elsevier Science
Subjects
Exact sciences and technology
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Transport processes
Theoretical study
Jump process
Stochastic process
Memory effect
Random variable
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Summary:A new stochastic description of random jump processes with memory is suggested. The method is based on the assumption that the overall jump rate is a supplementary random state variable. We assume that the joint probability for the jump rate as well as for other state variables fulfills a Markovian master equation. A particular case of our approach is equivalent to the use of a generalized master equation with an inhomogeneous term or of a continuous time random walk where the first jump has a special behavior. A comparison with the theory of age-dependent master equations allows us to clarify the physical meaning of the inhomogeneous term of the generalized master equation.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(91)90917-W