Abstract
For a given master equation of a discontinuous irreversible Markov process, we present the derivation of stochastically equivalent Langevin equations in which the noise is either multiplicative white generalized Poisson noise or a spectrum of multiplicative white Poisson noise. In order to achieve this goal, we introduce two new stochastic integrals of the Ito type, which provide the corresponding interpretation of the Langevin equations. The relationship with other definitions for stochastic integrals is discussed. The results are elucidated by two examples of integro-master equations describing nonlinear relaxation.
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Supported by National Science Foundation Grant CHE78-21460
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Hänggi, P. Langevin description of markovian integro-differential master equations. Z Physik B 36, 271–282 (1980). https://doi.org/10.1007/BF01325291
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DOI: https://doi.org/10.1007/BF01325291