Related papers: Analytic crossing probabilities for certain barrie…
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
Thermally activated escape over a potential barrier in the presence of periodic driving is considered. By means of novel time-dependent path-integral methods we derive asymptotically exact weak-noise expressions for both the instantaneous…
An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
We present a new method to compute the first crossing distribution in excursion set theory for the case of correlated random walks. We use a combination of the path integral formalism of Maggiore & Riotto, and the integral equation solution…
Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…
The conditional density of Brownian motion is considered given the max, B(t|\max), as well as those with additional information: B(t|close, max), B(t|close, max, min) and B(t|max, min) where the close is the final value: B(t=1)=c and t in…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The…
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 give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on the two-dimensional lattice. By `collision' we mean collision between the random walks as well as…
In this paper we investigate the boundary non-crossing probabilities of a fractional Brownian motion considering some general deterministic trend function. We derive bounds for non-crossing probabilities and discuss the case of a large…
The asymptotic probability distribution for a Brownian particle wandering in a 2D plane with random traps to enclose the algebraic area A by time t is calculated using the instanton technique.
The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the…
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or…