Related papers: Ergodicity of conditional McKean-Vlasov jump diffu…
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…
We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.…
In this work, we study ergodicity of continuous time Markov processes on state space $\mathbb{R}_{\geq 0} := [0,\infty)$ obtained as unique strong solutions to stochastic equations with jumps. Our first main result establishes exponential…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
As extensions to the corresponding results derived for time homogeneous McKean- Vlasov SDEs, the exponential ergodicity is proved for time-periodic distribution dependent SDEs in three different situations: 1) in the quadratic Wasserstein…
This paper establishes a verification theorem for impulse control problems involving conditional McKean-Vlasov jump diffusions. We obtain a Markovian system by combining the state equation of the problem with the stochastic Fokker-Planck…
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in…
We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove…
In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$, two unknown parameters. We suppose that the process is discretely observed at the…
The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems. The existing methods on the irreducibility of stochastic partial differential equations (SPDEs) and stochastic differential equations (SDEs)…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed balance. For the corresponding Fokker-Planck equation on a…
This work focuses on stability analysis of numerical solutions to jump diffusions and jump diffusions with Markovian switching. Due to the use of Poisson processes, using asymptotic expansions as in the usual approach of treating diffusion…
We provide an explicit rigorous derivation of a diffusion limit - a stochastic differential equation with additive noise - from a deterministic skew-product flow. This flow is assumed to exhibit time-scale separation and has the form of a…
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…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
We investigate a McKean-Vlasov stochastic differential equation with an additive common noise and in which the interaction is through the conditional expectation. We show that, in the presence of an additive individual noise, existence and…
We prove It{\^o}'s formula for the flow of measures associated with a jump process defined by a drift, an integral with respect to a Poisson random measure and with respect to the associated compensated Poisson random measure. We work in…