Related papers: Persistent search in confined domains: a velocity-…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target.…
This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…
Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest…
For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems 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…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
We study the target search of interacting Brownian particles in a finite domain, focusing on the effect of inter-particle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its…
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the…
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…
We consider random search processes alternating stochastically between diffusion and ballistic motion, in which the distribution function of ballistic motion directions varies from point to point in space. The specific space dependence of…
When greedy search algorithms encounter a local minima or plateau, the search typically devolves into a breadth-first search (BrFS), or a local search technique is used in an attempt to find a way out. In this work, we formally analyze the…
We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit…
We introduce a new class of first passage time optimization driven by threshold resetting, inspired by many natural processes where crossing a critical limit triggers failure, degradation or transition. In here, search agents are…
Under some weak conditions, the first-passage time of the Brownian motion to a continuous curved boundary is an almost surely finite stopping time. Its probability density function (pdf) is explicitly known only in few particular cases.…