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A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…

Statistical Mechanics · Physics 2007-05-23 Jean Pierre Boon , Patrick Grosfils , James F. Lutsko

We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.

Optimization and Control · Mathematics 2007-06-13 Tryphon T. Georgiou

The motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of…

Statistical Mechanics · Physics 2016-08-01 Muktish Acharyya

We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact…

Statistical Mechanics · Physics 2007-05-23 S. B. Yuste , Katja Lindenberg

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…

Statistical Mechanics · Physics 2022-06-29 Subhajit Acharya , Biman Bagchi

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…

Statistical Mechanics · Physics 2011-04-05 Annalisa Molini , Peter Talkner , Gabriel G. Katul , Amilcare Porporato

We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…

Neurons and Cognition · Quantitative Biology 2016-01-26 Vaibhav Srivastava , Philip Holmes , Patrick Simen

Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed…

Statistical Mechanics · Physics 2015-06-25 O. Benichou , M. Coppey , M. Moreau , P. H. Suet , R. Voituriez

We consider the general problem of the first passage distribution of particles whose displacements are subject to time delays. We show that this problem gives rise to a \emph{propagation-dispersion equation} which is obtained as the…

Statistical Mechanics · Physics 2009-11-10 Jean Pierre Boon , Patrick Grosfils , James F. Lutsko

We have random number of independent diffusion processes with absorption on boundaries in some region at initial time $t=0$. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to…

Probability · Mathematics 2016-09-07 Aniello Fedullo , Vitalii A. Gasanenko

We study the first exit time of a multi-dimensional fractional Brownian motion from unbounded domains. In particular, we are interested in the upper tail of the corresponding distribution when the domain is parabola-shaped.

Probability · Mathematics 2020-02-11 Frank Aurzada , Mikhail Lifshits

Estimates for exit time from an interval of length 2r before a prescribed time T are derived for solutions of a class of stochastic partial differential equations used to characterize two population models: super-Brownian motion and…

Probability · Mathematics 2023-02-24 Parisa Fatheddin

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following…

Probability · Mathematics 2012-04-26 Christophe Profeta

Liquid-gas phase transition in statistical mechanics is a long-standing dilemma not yet well explained. In this paper we propose a novel approach to this dilemma, by: 1). Putting forth a new space homogeneity assumption. 2). Giving a new…

Statistical Mechanics · Physics 2007-05-23 Yuan-Xing Gui

We obtain estimates for the weighted $L^1$-norm of the difference of two probability solutions to Kolmogorov equations in terms of the difference of the diffusion matrices and the drifts. Unlike the previously known results, our estimate…

Analysis of PDEs · Mathematics 2025-12-17 Vladimir I. Bogachev , Stanislav V. Shaposhnikov

We study the long-time behavior of the probability density Q_t of the first exit time from a bounded interval [-L,L] for a stochastic non-Markovian process h(t) describing fluctuations at a given point of a two-dimensional, infinite in both…

Statistical Mechanics · Physics 2008-01-28 G. Oshanin

Many physical processes depend on the time it takes a diffusing particle to find a target. Though this classical quantity is now well-understood in various scenarios, little is known if the diffusivity depends on the location of the…

Statistical Mechanics · Physics 2025-12-23 Hwai-Ray Tung , Sean D Lawley

In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…

Probability · Mathematics 2016-09-30 Noufel Frikha , Arturo Kohatsu-Higa , Libo Li

We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which…

Statistical Mechanics · Physics 2009-10-31 C. Henrique , G. Batrouni , D. Bideau

In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…

Probability · Mathematics 2016-11-08 Christoph Reisinger