Exact solution of evolution equation for randomly interrupted diffusion

An evolution equation of integro‐differential type for a one‐dimensional probability distribution of a linear process driven by additive randomly interrupted Gaussian white noise is exactly solved. A family of propagators for a probability distribution of the process is obtained. Selected examples o...

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Bibliographic Details
Published in:Journal of mathematical physics 1993-11, Vol.34 (11), p.5357-5366
Main Authors: L/uczka, Jerzy, Niemiec, Mariusz, Piotrowski, Edward
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
Mathematical methods in physics
Physics
Probability theory, stochastic processes, and statistics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Stochastic processes
Transport processes
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Summary:An evolution equation of integro‐differential type for a one‐dimensional probability distribution of a linear process driven by additive randomly interrupted Gaussian white noise is exactly solved. A family of propagators for a probability distribution of the process is obtained. Selected examples of a time‐dependent distribution are presented.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.530309