Related papers: First passage under restart with branching
Transport is an important function of networks. Studying transport efficiency sheds light on the dynamic processes occurring within various underlying structures and offers a wide range of applications. To construct networks with different…
In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…
We study the first-passage-time (FPT) properties of an active Brownian particle under stochastic resetting to its initial configuration, comprising its position and orientation, to reach an absorbing wall in two dimensions. Coupling a…
Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size…
In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution…
We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
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…
Random search for one or more targets in a bounded domain occurs widely in nature, with examples ranging from animal foraging to the transport of vesicles within cells. Most theoretical studies take a searcher-centric viewpoint, focusing on…
We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
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)…
Consider a stable L\'evy process $X=(X_t,t\geq 0)$ and let $T_x$, for $x>0$, denote the first passage time of $X$ above the level $x$. In this work, we give an alternative proof of the absolute continuity of the law of $T_x$ and we obtain a…
First passage distributions of semi-Markov processes are of interest in fields such as reliability, survival analysis, and many others. The problem of finding or computing first passage distributions is, in general, quite challenging. We…
Consider first passage percolation on $\mathbb{Z}^d$ with passage times given by i.i.d. random variables with common distribution $F$. Let $t_\pi(u,v)$ be the time from $u$ to $v$ for a path $\pi$ and $t(u,v)$ the minimal time among all…
We study the counting of level crossings for inertial random processes exposed to stochastic resetting events. We develop the general approach of stochastic resetting for inertial processes with sudden changes in the state characterized by…
Many tasks are subject to failure before completion. Two of the most common failure recovery strategies are restart and checkpointing. Under restart, once a failure occurs, it is restarted from the beginning. Under checkpointing, the task…