Related papers: Randomized First Passage Times
We study an inverse first-passage-time problem for Wiener process $X(t)$ subject to hold and jump from a boundary $c.$ Let be given a threshold $S>X(0) \ge c,$ and a distribution function $F$ on $[0, + \infty ).$ The problem consists in…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
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…
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…
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…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
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…
In this paper we consider a (reflected) Brownian motion with broken drift hitting a random boundary. Some dedicated calculations allow us to obtain the formula on the joint Laplace transform of the hitting time and hitting position. These…
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…
We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=\mu |x-x_0|$, where $\mu>0$ is the strength of the potential and $x_0>0$ is the…
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…
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.…
The inverse first passage time problem asks whether, for a Brownian motion $B$ and a nonnegative random variable $\zeta$, there exists a time-varying barrier $b$ such that $\mathbb{P}\{B_s>b(s),0\leq s\leq t\}=\mathbb{P}\{\zeta>t\}$. We…
Let $U$ be a domain, convex in $x$ and symmetric about the y-axis, which is contained in a centered and oriented rectangle $R$. \linebreak If $\tau_A$ is the first exit time of Brownian motion from $A$ and $A^+=A\cap \{(x,y):x>0\}$, it is…
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…
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…
We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of…
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…
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…
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…