Related papers: First-Extinction Law for Resampling Processes

We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction…

The homogeneous reconstructed evolutionary process is a birth-death process without observed extinct lineages. Each species evolves independently with the same diversification rates (speciation rate $\lambda(t)$ and extinction rate…

Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…

Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…

We examine the validity of the principle of mass conservation for solutions of some typical equations in the theory of nonlinear diffusion, including equations in standard differential form and also their fractional counterparts. In Part 1,…

For a smooth bounded domain $\Omega\subseteq\mathbb{R}^n$, $n\geq 3$, we consider the fast diffusion equation with critical sobolev exponent $$\frac{\partial w}{\partial\tau} =\Delta w^{\frac{n-2}{n+2}}$$ under Dirichlet boundary condition…

Both theoretical and applied economics have a great deal to say about many aspects of the firm, but the literature on the extinctions, or demises, of firms is very sparse. We use a publicly available data base covering some 6 million firms…

Epidemics unfold by means of a spreading process from each infected individual to a random number of secondary cases. It has been claimed that the so-called superspreading events in COVID-19 are governed by a power-law tailed distribution…

We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from…

The behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption $\partial_t u - \Delta_p u + |\nabla u|^{p-1} = 0$ in $(0, \infty) \times…

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…

For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…

This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law''…

It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…

We study a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are…

We present an analytical framework to study the first-passage (FP) and first-return (FR) distributions for the broad family of models described by the one-dimensional Fokker-Planck equation in finite domains, identifying general properties…

We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power $\alpha$,…

We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…

In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…