Related papers: On the exit-problem for self-interacting diffusion…
We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential $v(x)$ in a finite domain. We focus on the cases in which the external potential is confining, of the…
The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches…
Self-interacting diffusions are solutions to SDEs with a drift term depending on the process and its normalized occupation measure $\mu_t$ (via an interaction potential and a confinement potential). We establish a relation between the…
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…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
We consider a dynamical system described by the differential equation $\dot{Y}_t=-U'(Y_t)$ with a unique stable point at the origin. We perturb the system by the L\'evy noise of intensity $\varepsilon$ to obtain the stochastic differential…
We consider a model of branching Brownian motion with self repulsion. Self-repulsion is introduced via change of measure that penalises particles spending time in an $\e$-neighbourhood of each other. We derive a simplified version of the…
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
In this paper we develop some new variational principles for the exit time of non-symmetric diffusions from a domain. As applications, we give some comparison theorems and monotonicity law between different diffusions.
This paper investigates the boundary behaviour of potential-type integrals for the multi-term time-fractional diffusion equation (MTFDE) across the moving boundary. First, we establish the jump relation for the integral operator associated…
The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed $V$ along a direction that changes slowly by rotational diffusion, characterized by a coefficient $\Dr$.…
We study a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are…
Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…
Let \{B_t^H,t\geq0\} be a d-dimensional fractional Brownian motion. We prove that the approximation of the first-order derivative of self-intersection local time, defined as…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
We review and study a one-parameter family of functional transformations, denoted by $(S^{(\beta)})_{\beta\in \R}$, which, in the case $\beta<0$, provides a path realization of bridges associated to the family of diffusion processes…
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.…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…