Related papers: On $L_1$-distance between first exit times from tw…
We consider a particle diffusing outside a compact planar set and investigate its boundary local time $\ell_t$, i.e., the rescaled number of encounters between the particle and the boundary up to time $t$. In the case of a disk, this is…
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…
Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
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…
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…
This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and…
The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the…
We provide Large Deviation estimates for the bridge of a $d$-dimensional general diffusion process as the conditioning time tends to $0$ and apply these results to the evaluation of the asymptotics of its exit time probabilities. We are…
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
By using the large deviation principle, we investigate the expected exit time from the interval [-1,1] of a process of autoregressive type. The case when the autoregression function f is linear and the innovations have a normal distribution…
We review some of the theory relevant to passage times of one-dimensional L\'evy processes out of bounded regions, highlighting results that are useful in physical phenomena modelled by heavy-tailed L\'evy flights. The process is…
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.