Related papers: Integral Equations and the First Passage Time of B…

We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dimension higher than two. When at least one Brownian motion…

In this work we relate the density of the first-passage time of a Wiener process to a moving boundary with the three dimensional Bessel bridge process and a solution of the heat equation with a moving boundary. We provide bounds.

In this paper, we derive an integral representation for the density of the reciprocal of the first hitting time of the boundary of a wedge of angle $\pi/4$ by a radial Dunkl process with equal multiplicity values. Not only this…

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…

We study the target search of interacting Brownian particles in a finite domain, focusing on the effect of inter-particle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its…

We introduce the (path-valued) Brownian frame process whose evaluation at time t is the sample path of the underlying Brownian motion run from time t-1 to t. Due to its connections with Gaussian Volterra processes and SDDEs this is an…

In this paper, we study the classical problem of the first passage hitting density of an Ornstein--Uhlenbeck process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for…

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…

Consider a negatively drifted one dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time…

A class of algorithms in discrete space and continuous time for Brownian first passage time estimation is considered. A simple algorithm is derived that yields exact mean first passage times (MFPT) for linear potentials in one dimension,…

We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear…

We investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be…

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…

We discuss chains of interacting Brownian motions. Their time reversal invariance is broken because of asymmetry in the interaction strength between left and right neighbor. In the limit of a very steep and short range potential one arrives…

We consider stochastic differential equations driven by some Volterra processes. Under time reversal, these equations are transformed into past dependent stochastic differential equations driven by a standard Brownian motion. We are then in…

We consider a wide class of increasing L\'evy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in the literature. Classically failure time…

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with H\"older exponent greater than 1/2, we…

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We…

We study some limit theorems for the normalized law of integrated Brownian motion perturbed by several examples of functionals: the first passage time, the nth passage time, the last passage time up to a finite horizon and the supremum. We…

We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…