Related papers: On the asymptotic of exit problems for controlled …
We prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…
This paper studies, in dimensions greater than two, stationary diffusion processes in random environment which are small, isotropic perturbations of Brownian motion satisfying a finite range dependence. Such processes were first considered…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
It is well known that a regular diffusion on an interval $I$ without killing inside is uniquely determined by a canonical scale function $s$ and a canonical speed measure $m$. Note that $s$ is a strictly increasing and continuous function…
We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when…
First-passage properties of continuous stochastic processes confined in a 1--dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains…
Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
We provide Large Deviation estimates for the bridge of a $d$-dimensional general diffusion process as the conditioning time tends to $0$ and apply these results to the evaluation of the asymptotics of its exit time probabilities. We are…
We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the H\"older constant of the Hessian of…
Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of…
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…
In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…
In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, we solve the associated nonlinear eigenvalue problem for weakly coupled systems and…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
We extend the principles of information thermodynamics to study energy and information exchanges between coupled systems composed of one part undergoing a Markov jump process and another underdamped diffusion. We derive integral fluctuation…
IIn this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
This paper investigates a diffusion process in a narrow tubular domain with reflecting boundary conditions, where the geometry serves as a singular perturbation of an underlying graph in $\mathbb{R}^2$ or $\mathbb{R}^3$. The construction…