Related papers: Explicit Asymptotics on First Passage Times of Dif…
For a spectrally negative L\'evy process (snLp) $X$, killed according to a rate that is a function $\omega$ of its position, we analyse the exit probability of the one-sided upwards-passage problem. When $\omega$ is strictly positive, this…
We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion…
A frequency-based omni-temporal dispersion theory is developed to capture the transient interplay between diffusion, advection, and reaction during solute transport through porous media. Unlike classical asymptotic dispersion theories,…
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study…
We propose a new approximation for the distribution of the time of the first level $u$ crossing by the random process $\homV{s}-cs$, where $\homV{s}$, $s>0$, is compound renewal process and $c>0$. It is competitive with respect to existing…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
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…
We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on exact expansion of the backward master equation in cumulants. The…
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…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimised by introduction of a piecewise linear potential barrier. Analytical…
We examine the density functions of the first exit times of the Bessel process from the intervals [0,1) and (0,1). First, we express them by means of the transition density function of the killed process. Using that relationship we provide…
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…
The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…
The purpose of this work is the study of solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the…