相关论文: Integral Equations and the First Passage Time of B…

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…

For classical finite time horizon stopping problems driven by a Brownian motion \[V(t,x) = \sup_{t\leq\tau\leq0}E_{(t,x)}[g(\tau,W_{\tau})],\] we derive a new class of Fredholm type integral equations for the stopping set. For large problem…

We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We…

In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm is known and is based on an EM algorithm when involved functions are non-negative and integrable. With this algorithm we…

Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…

We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…

The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…

We obtain explicit solutions for the density $\varphi_T$ of the first-time $T$ that a one-dimensional Brownian process $B$ reaches the twice, continuously differentiable moving boundary $f$ and such that $f''(t)\geq 0$ for all $t\in…

We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…

This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…

We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions…

We prove that for a standard Brownian motion, there exists a first-passage-time density function through a locally H\"older continuous curve with exponent greater than 1/2. By using a property of local time of a standard Brownian motion and…

This paper is devoted to study a class of stochastic Volterra equations associated with fractional Brownian motion. We first prove the Driver type integration by parts formula and the shift Harnack type inequalities. As a direct…

Let $W$ be a standard Brownian motion with $W_0 = 0$ and let $b: \mathbb{R}_+ \to \mathbb{R}$ be a continuous function with $b(0) > 0$. The first passage time (from below) is then defined as \begin{align*} \tau := \inf \{ t \geq 0 \vert W_t…

We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…

We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…

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…

The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the…

We consider stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 . We first derive supremum norm estimates for the solution and its Malliavin derivative. We then show existence and…

We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction…