In standard planar first-passage percolation [11] each pair x and y of nearest-neighbor of Z has an edge connecting them and each edge is equipped with a non-negative random variable (passage time) which may be interpreted as the time it takes for an infection to be transmitted from x to y. We assume these random variables are i.i.d. with a continuous distribution F. The passage time t(γ) for a...

The concept of the ”transient effect” is examined in respect of a ”mean first passage time”. It is demonstrated that the time the fissioning system stays inside the barrier is much larger than suggested by the transient time, and that no enhancement of emission of neutrons over that given by Kramers’ rate formula ought to be considered.

A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return process in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the mo...

In this paper we use the method of images to derive the closed-form formula for the first passage time density of a timedependent Ornstein–Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation scheme to compute tight upper and lower bounds of the first passage time density through a fixed boundary. ...

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced. For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift ca...