相关论文: Quasistationarity and extinction for population pr…

Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-order quasi-stationary Mean Field Games system, which involves…

In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…

We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…

A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…

Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…

We study a two parameter ($u,p$) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the…

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…

Density dependent Markov population processes in large populations of size $N$ were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution of the differential equations that describe their average…

We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states,…

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…

We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to…

We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…

In this work we suggest and consider an original, simple mathematical model of a "quasi-rapid" extinction population dynamics. It describes a decrease and final extinction of the population of one prey species by a "quasi-rapid" interaction…

We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are applied to multi-dimensional birth and death…

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…

We consider the following evolutionary Hamilton-Jacobi equation with initial condition: \begin{equation*} \begin{cases} \partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x), \end{cases} \end{equation*} where $\phi(x)\in…

The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…

We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…

In this paper we consider the global qualitative properties of a stochastically perturbed logistic model of population growth. In this model, the stochastic perturbations are assumed to be of the white noise type and are proportional to the…