Related papers: Analytic crossing probabilities for certain barrie…
Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in R^d. Let Z(t) denote the path integral of v along the path of a Brownian bridge in R^d which runs for time t, starting at x and ending at y. As t->infty, it is…
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
We study the first-passage-time (FPT) properties of active Brownian particles to reach an absorbing wall in two dimensions. Employing a perturbation approach we obtain exact analytical predictions for the survival and FPT distributions for…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…
The paper presents two results. The first one provides separate conditions for the upper and lower estimate of the distribution of the exit time from balls of a random walk on a weighted graph. The main result of the paper is that the lower…
A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…
We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\Gamma$ defined by this action for some fixed generating set. For a probability measure $\mu$ on $G$ with a finite first moment we show that if the…
Aldous and Pitman (1994) studied asymptotic distributions, as n tends to infinity, of various functionals of a uniform random mapping of a set of n elements, by constructing a mapping-walk and showing these mapping-walks converge weakly to…
We present an exact solution for the probability density function $P(\tau=t_{\min}-t_{\max}|T)$ of the time-difference between the minimum and the maximum of a one-dimensional Brownian motion of duration $T$. We then generalise our results…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that…
We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to…
For the one-dimensional Brownian motion $B=(B_t)_{t\ge 0}$, started at $x>0$, and the first hitting time $\tau=\inf\{t\ge 0:B_t=0\}$, we find the probability density of $B_{u\tau}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its way…
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
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 provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this…