An Interdisciplinary Journal

* 2006, Vol.9, No.1, pp.75-80*

Generalized master equation has been derived for the
probability density function *P(X,t)* within the following
assumptions: (i) a time realization of the stochastic process
*X(t)* can be represented as a sequence of intervals of free
motion (event *A*) interrupted by collisions (event *B*); (ii)
durations of the events *A* and *B* are governed by arbitrary
distributions ;
(iii) the time evolution of
*X(t)* during the events *A* and *B* is described by the
time-independent Liouville operators . The approach
generalizes the standard Markovian master equations to non-instantaneous
collisions and non-Poissonian collision statistics.

*Key words: *
generalized master equation, non-poissonian collision
statistics, non-instantaneous collisions

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Last updated: *April 25, 2006*