Related papers: On $L_1$-distance between first exit times from tw…
It is given an effective upper estimate of expectation of |T_1-T_2|, where T_1 and T_2 are the first exit times from a region for two vector diffusion processes.
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…
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 establish general moment estimates for the discrete and continuous exit times of a general It\^o process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
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 purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.
We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall.…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…
We compute the joint distribution of the first times a linear diffusion makes an excursion longer than some given duration above (resp. below) some fixed level. In the literature, such stopping times have been introduced and studied in the…
We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field, when we condition on the event that the particle reaches the target for flow away…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
The main result in this paper is a variational formula for the exit rate from a bounded domain for a diffusion process in terms of the stationary law of the diffusion constrained to remain in this domain forever. Related results on the…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an integration by parts formula for the first exit time of…
The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for…