Related papers: Stochastic Functional Kolmogorov Equations (I): Pe…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
We consider the setting of either a general non-local branching particle process or a general non-local superprocess. Under the assumption that the mean semigroup has a Perron-Frobenious type behaviour in combination with a regularly…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
We analyze infinite-dimensional non-linear degenerate stochastic differential equations with multiplicative noise. First, essential m-dissipativity of their associated Kolmogorov backward generators on $L^2(\mu^{\Phi})$ defined on smooth…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
In 1974 Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let data be finite binary strings and models be finite sets of binary strings. Consider model classes consisting of models of given maximal…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: \[ \begin{cases} \partial_{t}u(t,\phi)+\mathcal{L}u(t,\phi)+f(t,\phi,u(t,\phi),\partial_{x}u(t,\phi)…
The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed "spin-$\frac12$ functions" and later "Kolmogorovian models", which employs a nonstandard notion of probability. We describe…
We present an effective evolution equation for a coarse-grained distribution function of a long-range-interacting system preserving the symplectic structure of the non-collisional Boltzmann, or Vlasov, equation. We first derive a general…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These…
In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique,…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
This is the fourth paper, the last one, on solution to the problem of absence of detailed balance in nonequilibrium processes. It is an approach based on another known universal dynamics: The evolutionary dynamics first conceived by Darwin…