Hitting time
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First passage under stochastic resetting in an interval Open
We consider a Brownian particle diffusing in a one-dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive stu…
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Subdiffusive continuous-time random walks with stochastic resetting Open
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk scheme and independent resetting events generated uniformly in time according to the…
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A new remaining useful life estimation method for equipment subjected to intervention of imperfect maintenance activities Open
As the key part of Prognostics and Health Management (PHM), Remaining Useful Life (RUL) estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance acti…
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Characterization of cutoff for reversible Markov chains Open
A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. We consider reversible lazy chains. We prove a necessary and sufficient condition for the occ…
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Faster Algorithms for Computing the Stationary Distribution, Simulating Random Walks, and More Open
In this paper, we provide faster algorithms for computing variousfundamental quantities associated with random walks on a directedgraph, including the stationary distribution, personalized PageRankvectors, hitting times, and escape probabi…
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Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility Open
We study the hitting times of Markov processes to target set G, starting from a reference configuration x0 or its basin of attraction and we discuss its relation to metastability.
\nThree types of results are reported: (1) A general theory…
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A characterization of $L_{2}$ mixing and hypercontractivity via hitting times and maximal inequalities Open
There are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the $L_{2}$ m…
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First Hitting Times to Intermittent Targets Open
In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we stud…
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Conditioned, quasi-stationary, restricted measures and escape from metastable states Open
We study the asymptotic hitting time $\\tau^{(n)}$ of a family of Markov processes $X^{(n)}$ to a target set $G^{(n)}$ when the process starts from a “trap” defined by very general properties. We give an explicit description of the law of …
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Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set Open
This paper presents improved deterministic distributed algorithms, with O(log n)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set…
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Fast Bidirectional Probability Estimation in Markov Models Open
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
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Finding a marked node on any graph via continuous-time quantum walks Open
Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$. How…
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Speed of coming down from infinity for birth-and-death processes Open
We describe in detail the speed of `coming down from infinity' for birth-and-death processes which eventually become extinct. Under general assumptions on the birth-and-death rates, we firstly determine the behavior of the successive hitti…
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Random walks on graphs: new bounds on hitting, meeting, coalescing and returning Open
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities Pt(x, x) and the maximum expected hitting time thit, both in terms of the relaxation time. We also prove a discretetime v…
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Hitting and trapping times on branched structures Open
In this work we consider a simple random walk embedded in a generic branched structure and we find a close-form formula to calculate the hitting time H(i,f) between two arbitrary nodes i and j. We then use this formula to obtain the set of…
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On coalescence time in graphs: When is coalescing as fast as meeting?: Extended Abstract Open
Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a …
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Quantum fast hitting on glued trees mapped on a photonic chip Open
Quantum walks on graphs play an important role in the field of quantum algorithms. Fast hitting is one of the properties that quantum walk algorithms can utilize to outperform classical random walk algorithms. Fast hitting refers to a part…
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Remaining useful life prediction for a nonlinear multi-degradation system with public noise Open
To predict the remaining useful life (RUL) for a class of nonlinear multi-degradation systems, a method is presented. In the real industrial processes, systems are usually composed by several parts or components, and these parts or compone…
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Entrance and exit at infinity for stable jump diffusions Open
In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $-\\infty \\leq a<b\\leq \\infty $ in terms of their ability to access the boundary (Feller’s test for explosions) and to enter the interior fr…
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An invariance principle for branching diffusions in bounded domains Open
We study branching diffusions in a bounded domain $D$ of $\\mathbb{R}^d$ in\nwhich particles are killed upon hitting the boundary $\\partial D$. It is known\nthat any such process undergoes a phase transition when the branching rate\n$\\be…
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Tail bounds on hitting times of randomized search heuristics using variable drift analysis Open
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing, etc . The vast majority of existing drift theorems yield b…
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The First-passage Time of the Brownian Motion to a Curved Boundary: an Algorithmic Approach Open
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Distribution of the span of one-dimensional confined random processes before hitting a target Open
We derive the distribution of the number of distinct sites visited by a random walker before hitting a target site of a finite one-dimensional (1D) domain. Our approach holds for the general class of Markovian processes with connected span…
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Biased Continuous-Time Random Walks with Mittag-Leffler Jumps Open
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connect…
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On the First Hitting Time Density of an Ornstein-Uhlenbeck Process Open
In this paper, we study the classical problem of the first passage hitting density of an Ornstein--Uhlenbeck process. We give two complementary (forward and backward) formulations of this problem and provide semi-analytical solutions for b…
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A Unified Framework of Quantum Walk Search Open
Many quantum algorithms critically rely on quantum walk search, or the use of quantum walks to speed up search problems on graphs. However, the main results on quantum walk search are scattered over different, incomparable frameworks, such…
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Oil-based maintenance interval optimization for power-shift steering transmission Open
The concentration of micron-size particles in used oil is generally obtained by atomic emission spectrometry. These accurate results can be considered as the most important index for real-time reliability evaluation including failure predi…
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Strongly constrained stochastic processes: the multi-ends Brownian bridge Open
In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018))\nestablished that the distribution of the first hitting times for a diffusing\nparticle subject to hitting an absorber is independent of the direction of the\nexterna…
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First hitting times between a run-and-tumble particle and a stochastically gated target Open
We study the statistics of the first hitting time between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of…
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On the probability of hitting the boundary for Brownian motions on the SABR plane Open
Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models???related to the SABR model in mathematical finance???which can be obtained by geometry-preserving transformations, an…