Related papers: Excursion theory for the Wright-Fisher diffusion
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
Understanding fluctuations of observables across stochastic trajectories is essential for various fields of research, from quantum thermal machines to biological motors. We introduce a framework to analyze the statistics of counting…
We introduce and study branching interval partition diffusions in their natural generality. We let interval widths evolve independently according to a general real-valued diffusion subject only to conditions that ensure finite lifetimes of…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
We analyze simple random walk on a supercritical Galton-Watson tree, where the walk is conditioned to return to the root at time $2n$. Specifically, we establish the asymptotic order (up to a constant factor) as $n\to\infty$, of the maximal…
We introduce a class of continuous planar processes, called "semimartingales on rays", and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such planar processes are…
We analyse a model that describes the propagation of many pathogens within and between many species. A branching process approximation is used to compute the probability of disease outbreaks. Special cases of aquatic environments with two…
Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. Continue until the first entry is 1. This process imposes a…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
A Walsh diffusion on Euclidean space moves along each ray from the origin, as a solution to a stochastic differential equation with certain drift and diffusion coefficients, as long as it stays away from the origin. As it hits the origin,…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction term on the existence and…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone…
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We study the analogue of Poisson ensembles of Markov loops ('loop soups') in the setting of one-dimensional diffusions. We give a detailed description of the corresponding intensity measure. The properties of this measure on loops lead us…