Related papers: Large deviations for slow-fast processes on connec…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…
Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value…
This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…
We consider generalized gradient systems with rate-independent and rate-dependent dissipation potentials. We provide a general framework for performing a vanishing-viscosity limit leading to the notion of parametrized and true…
This paper investigates an averaging principle for stochastic Klein-Gordon equation with a fast oscillation arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. Stochastic averaging…
We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
We consider a system of stochastic interacting particles in $\mathbb{R}^d$ and we describe large deviations asymptotics in a joint mean-field and small-noise limit. Precisely, a large deviations principle (LDP) is established for the…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities or criticalities, where the roof function defining the…
In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…
The paper is devoted to studying the asymptotics of the family $(\mu^\varepsilon)$ of stationary measures of the Markov process generated by the flow of stochastic 2D Navier-Stokes equation with smooth white noise. By using the large…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…