相关论文: Quasistationarity and extinction for population pr…

The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…

In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is…

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no…

The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the…

In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…

Assume $M$ is a closed, connected and smooth Riemannian manifold. We consider the evolutionary Hamilton-Jacobi equation \begin{equation*} \left\{ \begin{aligned} &\partial_t u(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\quad (x,t)\in…

We re-analyze the quasi-linear self consistent dynamics for the beam-plasma instability, by comparing the theory predictions to numerical simulations of the corresponding Hamiltonian system. While the diffusive features of the asymptotic…

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…

In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and…

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…

After reviewing the behavioral studies of working memory and of the cellular substrate of the latter, we argue that metastable states constitute candidates for the type of transient information storage required by working memory. We then…

We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and…

We construct the quasi-stationary (QS) distribution for two models of heterogeneous catalysis having two absorbing states: the ZGB model for the oxidation of CO, and a version with noninstantaneous reactions. Using a mean-field-like…

In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means…

We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…

We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and…

This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…