Related papers: Some examples of first exit times

We obtain some integrability properties and some limit theorems for the exit time from a cone of a planar Brownian motion, and we check that our computations are correct via Bougerol's identity.

The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…

We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an…

This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…

Let $\{X_i(t),t\ge0\}, i=1,2$ be two standard fractional Brownian motions being jointly Gaussian with constant cross-correlation. In this paper we derive the exact asymptotics of the joint survival function $$…

The motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of…

We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objective is to compute the expected perimeter of this convex hull, thereby complementing recent results on the convex hull of…

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…

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…

This paper considers the class of L\'evy processes that can be written as a Brownian motion time changed by an independent L\'evy subordinator. Examples in this class include the variance gamma model, the normal inverse Gaussian model, and…

In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven…

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…

Let $\tau_{D}(Z) $ be the first exit time of iterated Brownian motion from a domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[\tau_{D}(Z) >t]$ be its distribution. In this paper we establish the exact asymptotics of…

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…

We study the dynamics of the outliers for a large number of independent Brownian particles in one dimension. We derive the multi-time joint distribution of the position of the rightmost particle, by two different methods. We obtain the two…

We consider a collection of balls in Euclidean space and the problem of determining if Brownian motion has a positive probability of avoiding all the balls

We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general…

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic…

Iterated Brownian motion $Z_{t}$ serves as a physical model for diffusions in a crack. If $\tau_{D}(Z) $ is the first exit time of this processes from a domain $D \subset \RR{R}^{n}$, started at $z\in D$, then $P_{z}[\tau_{D}(Z)>t]$ is the…

Let $A_t$ be an $\alpha$-stable symmetric process, $0<\alpha\leq 2$, on $\mathbb{R}^d$ and $D\subset \mathbb{R}^d$ be a bounded domain. This paper presents a proof, based on the classical Brascamp-Lieb-Luttinger inequalities for multiple…