Related papers: Uniqueness of First Passage Time Distributions via…

Let $W$ be a standard Brownian motion with $W_0 = 0$ and let $b\colon[0,\infty) \to \mathbb{R}$ be a continuous function with $b(0) > 0$. In this article, we look at the classical First Passage Time (FPT) problem, i.e., the question of…

The distribution of the first-passage time (FPT)$T_a$ for a Brownian particle with drift $\mu$ subject to hitting an absorber at a level $a>0$ is well-known and given by its density $\gamma(t) = \frac{a}{\sqrt{2 \pi t^3} } e^{-\frac{(a-\mu…

In this article we study a problem related to the first passage and inverse first passage time problems for Brownian motions originally formulated by Jackson, Kreinin and Zhang (2009). Specifically, define $\tau_X = \inf\{t>0:W_t + X \le…

For drifted Brownian motion $X(t)= x - \mu t + B_t \ (\mu >0)$ starting from $x>0,$ we study the joint distribution of the first-passage time below zero, $\tau(x),$ and the first-passage area, $A(x),$ swept out by $X$ till the time…

We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A first-passage functional is defined as $V=\int_0^{t_f} Z[x(\tau)]$ where $t_f$ is the…

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…

The prediction of arrival time or first passage time statistics of a quantum particle is an open problem, which challenges the foundations of quantum theory. One of the most promising and insightful approaches to this problem stems from the…

The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…

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…

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…

First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion.…

We study the distribution of first-passage functionals ${\cal A}= \int_0^{t_f} x^n(t)\, dt$, where $x(t)$ is a Brownian motion (with or without drift) with diffusion constant $D$, starting at $x_0>0$, and $t_f$ is the first-passage time to…

Nearly fifty years after the introduction of skew Brownian motion by It\^o and McKean (1963), the first passage time distribution remains unknown. In this paper, we generalize results of Pitman and Yor (2001) and Cs\'aki and Hu (2004) to…

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the…

The classical inverse first passage time problem asks whether, for a Brownian motion $(B_t)_{t\geq 0}$ and a positive random variable $\xi$, there exists a barrier $b:\mathbb{R}_+\to\mathbb{R}$ such that $\mathbb{P}\{B_s>b(s), 0\leq s \leq…

Let X_t be a subordinate Brownian motion, and suppose that the Levy measure of the underlying subordinator has completely monotone density. Under very mild conditions, we find integral formulae for the tail distribution P(\tau_x > t) of…

It is considered the integrated process $X(t)= x + \int _0^t Y(s) ds ,$ where $Y(t)$ is a Gauss-Markov process starting from $y.$ The first-passage time (FPT) of $X$ through a constant boundary and the first-exit time of $X$ from an…

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…

First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…