FIRST-PASSAGE TIME DISTRIBUTIONS FOR LINEAR CHAIN SEGMENTS WITH GENERAL SITE-DEPENDENT WAITING-TIME DISTRIBUTIONS*)

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Abstract

First-passage time distributions (FPTD) of the arrival of a walk at a terminal site of a finite linear chain are considered, where the individual transition processes between the sites are specified by rather general waiting-time distributions. An exact expression for the first-passage time distribution can be given in Laplace space in terms of finite continued fractions. The circumstances under which the calculation of FPTD by this technique offers advantages over conventional calculations via master equations are discussed and possible applications to systems of biophysical interest are indicated.

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