相关论文: Martingales and first passage times of AR(1) seque…

We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…

The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in…

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…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions…

We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets…

We determine the asymptotic speed of the first-passage percolation process on some ladder-like graphs (or width-2 stretches) when the times associated with different edges are independent and exponentially distributed but not necessarily…

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 derive general bounds on the probability that the empirical first-passage time $\overline{\tau}_n\equiv \sum_{i=1}^n\tau_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the…

We introduce and study a class of abstract continuous action minimization problems that generalize continuous first and last passage percolation. In this class of models a limit shape exists. Our main result provides a framework under which…

In this paper, we study the maximal edge-traversal time (simply we call maximal weight hereafter) on the optimal paths in the first passage percolation for several edge distributions, including the Pareto and Weibull distributions. It is…

This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…

We consider the first passage percolation model on the ${\bf Z}^d$ lattice. In this model, we assign independently to each edge $e$ a non-negative passage time $t(e)$ with a common distribution $F$. Let $a_{0,n}$ be the passage time from…

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…

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…

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,…

A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…

We consider standard first-passage percolation on $\Z^d$. Let $e_1$ be the first coordinate vector. Let $a(n)$ be the expected passage time from the origin to $ne_1$. In this short paper, we note that $a(n)$ is increasing under some strong…

A general theory is derived for the moments of the first passage time of a one-dimensional Markov process in presence of a weak time-dependent forcing. The linear corrections to the moments can be expressed by quadratures of the potential…

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…