相关论文: First-passage properties of the jump process with …

How long a stochastic process survives before leaving a domain depends not only on its intrinsic dynamics but also on how it is observed. Classical first-passage theory assumes continuous monitoring with absorbing boundaries…

We derive the first-passage-time statistics of a Brownian motion driven by an exponential time-dependent drift up to a threshold. This process corresponds to the signal integration in a simple neuronal model supplemented with an…

In one and two dimensions, the first-passage time for a diffusing particle in the presence of a radial potential flow to hit a sphere, conditioned on actually hitting the sphere, is independent of the sign of the drift. Moreover, the…

We study the behavior of independent and stationary increments jump processes as they approach fixed thresholds. The exact crossing time is unavailable because the real-time information about successive jumps is unknown. Instead, the…

We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by the space-fractional spectral Fokker-Planck equation. This…

We investigate the first-passage properties of nearest-neighbor hopping on a finite interval with disordered hopping rates. We develop an approach that relies on the backward equation, in conjunction with probability generating functions,…

We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…

For a given barrier $S$ and a one-dimensional jump-diffusion process $X(t),$ starting from $x<S,$ we study the probability distribution of the integral $A_S(x)= \int_0 ^ {\tau_S(x)}X(t) \ dt$ determined by $X(t)$ till its first-crossing…

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average…

The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…

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…

A well known connection between first-passage probability of random walk and distribution of electrical potential described by Laplace equation is studied. We simulate random walk in the plane numerically as a discrete time process with…

We consider multidimensional random walks in pyramids, which by definition are cones formed by finite intersections of half-spaces. The main object of interest is the survival probability $\mathbb{P}(\tau>n)$, $\tau$ denoting the first exit…

The first passage statistics of a continuous time random walker with Poisson distributed jumps on one and two dimensional infinite lattices is investigated. An exact expression for the probability of first return to the origin in one…

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…

These notes are based on the lectures that I gave (virtually) at the Bruneck Summer School in 2021 on first-passage processes and some applications of the basic theory. I begin by defining what is a first-passage process and presenting the…

Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the…

In this paper a class of Ornstein--Uhlenbeck processes driven by compound Poisson processes is considered. The jumps arrive with exponential waiting times and are allowed to be two-sided. The jumps are assumed to form an iid sequence with…

We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage…