Related papers: First-passage times for random walks in bounded do…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
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…
Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory…
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…
As known, the commonly-utilized ways to determine mean first-passage time $\overline{\mathcal{F}}$ for random walk on networks are mainly based on Laplacian spectra. However, methods of this type can become prohibitively complicated and…
We present a closed-form expression for the survival probability of a biased random walker to first reach a target site on a 1D lattice. The expression holds for any step number $N$ and is computationally faster than non-closed-form results…
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…
We introduce a general approach for the study of the collective dynamics of non-interacting random walkers on connected networks. We analyze the movement of $R$ independent (Markovian) walkers, each defined by its own transition matrix. By…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions…
In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study…
General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…
We investigate the dynamics of simultaneous random walkers with resetting on networks and derive exact analytical expressions for the mean first-encounter times of Markovian random walkers. Specifically, we consider two cases for the…
We study the first-passage-time (FPT) properties of an active Brownian particle under stochastic resetting to its initial configuration, comprising its position and orientation, to reach an absorbing wall in two dimensions. Coupling a…
A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with…
We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of $N$ nodes of degree $c \ge 3$. Starting from a random initial node at time $t=0$, at each time…
A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating…
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…
This paper analyzes a method to approximate the first passage time probability density function which turns to be particularly useful if only sample data are available. The method relies on a Laguerre-Gamma polynomial approximation and…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The…