Related papers: A first passage problem for a Poisson counting pro…
This paper briefly presents an order statistic approach to the time distribution of the first detected event after a primary avalanche breakdown from a mixture of correlated and dark counting processes. The well-known order statistic…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…
Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…
We consider the so-called frog model with random initial configurations. The dynamics of this model is described as follows: Some particles are randomly assigned on any site of the multidimensional cubic lattice. Initially, only particles…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
We develop walk-on-sphere for fractional Poisson equations with Dirichilet boundary conditions in high dimensions. The walk-on-sphere method is based on probabilistic represen tation of the fractional Poisson equation. We propose effcient…
We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter…
In recent years, it has been well-established that adding a restart mechanism can alter the firstpassage statistics of a stochastic processes in useful and interesting ways. Though different mecha-nisms have been investigated, we derive a…
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…
We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt…
General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…
We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate…
Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the…
We investigate the first passage time beyond a barrier located at $b\geq0$ of a random walk with independent and identically distributed jumps, starting from $x_0=0$. The walk is subject to stochastic resetting, meaning that after each step…
S. G. Kou and H. Wang [First Passage times of a Jump Diffusion Process \textit{Ann. Appl. Probab.} {\bf 35} (2003) 504--531] give expressions of both the (real) Laplace transform of the distribution of first passage time and the (real)…
The ``first passage-time'' (FPT) problem is an important problem with a wide range of applications in mathematics, physics, biology and finance. Mathematically, such a problem can be reduced to estimating the probability of a (stochastic)…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…
We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed…
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random "searcher" to find a "target." The important timescale in a variety of biophysical systems is the time…