Related papers: Stochastic Extinction, An Average Lyapunov Functio…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
A Markov-switching observation-driven model is a stochastic process $((S_t,Y_t))_{t \in \mathbb{Z}}$ where $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov chain on a finite set and $(Y_t)_{t \in \mathbb{Z}}$ is an observed stochastic…
We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in…
In this paper, we consider the stochastic averaging principle and stability for multi-valued McKean-Vlasov stochastic differential equations with jumps. First, under certain averaging conditions, we are able to show that the solutions of…
We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…
We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a…
In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…