Dirichlet boundary conditions for a class of non-Markovian Gaussian stochastic processes
Varying conditions at boundaries can give rise to interesting effects on a stochastic system. For example, the first passage time of a non-Markovian stochastic process with boundaries has many practical applications. In this talk, we consider a class of non-Markovian white noise processes that has recently been applied to various complex systems ranging in size from nanoscales to gigameters. The probability density function (PDF) under Dirichlet conditions for this class of stochastic processes with memory is evaluated in closed form using white noise analysis. The PDF that vanishes at a boundary is then used to calculate physically interesting properties such as the survival probability and first passage time of fluctuating observables. In particular, we obtain the first passage time density for stochastic processes with different types of memory behavior.