Mean first passage time for a Markovian jumping process

Details Mean first passage time for a Markovian jumping process Mean first passage time for a Markovian jumping process

2007-10-15

arxiv.org/abs/0710.2686v1

Acta Phys. Pol. B38, (2007) 3119

Physics

Condensed Matter

Statistical Mechanics

13 pages, 6 figures

Scientific paper

We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean first passage time (MFPT) which appears always finite, also for the subdiffusive case. Then, for the case of the jumping-size distribution in form of the L\'evy distribution, we determine the probability density distributions and MFPT by means of numerical simulations. Dependence of the results on process parameters, as well as on the L\'evy distribution width, is discussed.

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