Related papers: Statistics of bounded processes driven by Poisson …

The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with $H>\tfrac{1}{2}$. For this, we summarise the theory of fractional white noise and prove a fundamental $L^2$-estimate for…

In this paper, we consider a quasi-linear stochastic heat equation on $[0,1]$, with Dirichlet boundary conditions and controlled by the space-time white noise. We formally replace the random perturbation by a family of noisy inputs…

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…

We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here,…

We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…

This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein's method with the Malliavin calculus of variations…

The tails of prehistory probability density in nonlinear multistable stochastic systems driven by white Gaussian noise, which has been a subject of recent study, are analyzed by employing the concepts of nonstationary optimal fluctuations.…

We set up a general formalism for models of spontaneous wave function collapse with dynamics represented by a stochastic differential equation driven by general Gaussian noises, not necessarily white in time. In particular, we show that the…

We present a generalized linear response theory for mixed jump-diffusion models -- combining Gaussian and L\'evy noise interacting with nonlinear dynamics -- by deriving comprehensive response formulas accounting for perturbations to both…

White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…

We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to…

In this paper we study the effect of stochastic perturbations on a common type of moving boundary value PDE's which endorse Stefan boundary conditions, or Stefan problems, and show the existence and uniqueness of the solutions to a number…

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…

We study a family of mean field games with a state variable evolving as a multivariate jump diffusion process. The jump component is driven by a Poisson process with a time-dependent intensity function. All coefficients, i.e. drift,…

Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…

We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated…

We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of…

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

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…