Related papers: First passage time law for some jump-diffusion pro…
We study analytically and numerically the mean fastest first-passage time (fFPT) to an immobile target for an ensemble of $N$ independent finite-speed random searchers driven by dichotomous noise and described by the telegrapher's equation.…
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the…
Let us consider a real L\'evy process X whose transition probabilities are absolutely continuous and have bounded densities. Then the law of the past supremum of X before any deterministic time t is absolutely continuous on (0,\infty). We…
With the help of the methods developed in our previous article [Schmitz, to appear in "Annales de l'I.H.P. Prob. & Stat.], we highlight condition (T) as a source of new examples of 'ballistic' diffusions in a random environment when d>1…
In this paper we study the joint distributions of the telegraph process and its maximum conditioned on the number of changes of direction and the initial velocity. We prove that in the case of positive starting velocity, a form of the…
The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over…
Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($\tau_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
We study the survival probability and the corresponding first passage time density of fractional Brownian motion confined to a two-dimensional open wedge domain with absorbing boundaries. By analytical arguments and numerical simulation we…
We investigate theoretically and experimentally the first passage-time properties of a spherical Brownian particle that is harmonically trapped at thermal equilibrium in a fluid at constant temperature. By using the overdamped version of…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
We determine how long a diffusing particle spends in a given spatial range before it dies at an absorbing boundary. In one dimension, for a particle that starts at $x_0$ and is absorbed at $x=0$, the average residence time in the range…
The first-return time is the time that it takes a random walker to go back to the initial position for the first time. We study the first-return time when random walkers perform fractional kinetics, specifically fractional diffusion, that…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary $t\mapsto a+bt,\ a\geq 0,\,b\in \R,$ by a reflecting Brownian motion. The main tool hereby is Doob's formula which gives the probability…
We investigate a novel first-passage percolation model, referred to as the Brochette first-passage percolation model, where the passage times associated with edges lying on the same line are equal. First, we establish a point-to-point…
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…
The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…