Related papers: Boundary crossing probabilities for diffusions wit…

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…

We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…

The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…

Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…

Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit…

The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…

We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for…

We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…

This article introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times, to an upper hard wall barrier and to a lower absorbing…

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with…

We propose a discrete time discrete space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of…

We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…

We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…

We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…

The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic processwith continuous variables, and important results can be explicitly found from…