Related papers: Mean exit time for diffusion on irregular domains
We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…
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…
We study the inverse boundary crossing problem for diffusions. Given a diffusion process $X_t$, and a survival distribution $p$ on $[0,\infty)$, we demonstrate that there exists a boundary $b(t)$ such that $p(t)=\mathbb{P}[\tau >t]$, where…
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…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed…
We compute the mean first passage time (MFPT) for a Brownian particle inside a two-dimensional disk with reflective boundaries and a small interior trap that is rotating at a constant angular velocity. The inherent symmetry of the problem…
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…
We provide an exact formula for the mean first-passage time (MFPT) to a target at the origin for a single particle diffusing on a $d$-dimensional hypercubic {\em lattice} starting from a fixed initial position $\vec R_0$ and resetting to…
This paper deals with the three-dimensional narrow escape problem in dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian…
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…
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…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…
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…
We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force-fields and chemotactic-fields, giving rise…