First passage time for some stationary processes

On the Asymptotic Behavior of First Passage Time Densities for Stationary Gaussian Processes and Varying Boundaries∗

Making use of a Rice-like series expansion, for a class of stationary Gaussian processes the asymptotic behavior of the first passage time probability density function through certain time-varying boundaries, including periodic boundaries, is determined. Sufficient conditions are then given such that the density asymptotically exhibits an exponential behavior when the boundary is either asympto...

Asymptotic Behaviour of First Passage Time Distributions for Lévy Processes

On some transformations of bilateral birth–and–death processes with applications to first passage time evaluations

A method yielding simple relationships among bilateral birth–and–death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first–passage–time densities and ultimate crossing probabilities are mutually related by some product–form expressions.

First Passage Problems for Asymmetric Wiener Processes

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T .

First Passage Distributions for Long Memory Processes

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...