Related papers: Tracking a Random Walk First-Passage Time Through …

The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…

The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…

The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…

The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…

We consider a variation of the Generalized Excited Random Walk (GERW) in dimension $d\ge 2$ where the lower bound on the drift for excited jumps is time-dependent and decays to zero. We show that if the lower bound decays slower that…

The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…

We study the statistics of the first passage of a random walker to absorbing subsets of the boundary of compact domains in different spatial dimensions. We describe a novel diagnostic method to quantify the trajectory-to-trajectory…

We consider the slow movement of randomly biased random walk $(X_n)$ on a supercritical Galton--Watson tree, and are interested in the sites on the tree that are most visited by the biased random walk. Our main result implies tightness of…

In this paper, we consider the statistical inference of the drift parameter $\theta$ of non-ergodic Ornstein-Uhlenbeck~(O-U) process driven by a general Gaussian process $(G_t)_{t\ge 0}$. When $H \in (0, \frac 12) \cup (\frac 12,1) $ the…

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these…

This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov State Models, known as local-equilibrium (LE). We show that for a…

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…

The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…

We study the $\beta$ analogue of the nonintersecting Poisson random walks. We derive a stochastic differential equation of the Stieltjes transform of the empirical measure process, which can be viewed as a dynamical version of the…

We revisit the simple lattice random walk (P\'{o}lya walk) and the Sisyphus random walk in $\mathbb{Z}$, in the presence of random restarts. We use a relatively direct approach namely First passage under restart for discrete space and time…

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on {0,1,2,...}, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results…

We investigate the first-passage properties of a jump process with a constant drift, focusing on two key observables: the first-passage time $\tau$ and the number of jumps $n$ before the first-passage event. By mapping the problem onto an…

A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…