Related papers: Ergodic theory for SDEs with extrinsic memory
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial…
A stochastic variational inequality is proposed to model an elasto-plastic oscillator excited by a filtered white noise. We prove the ergodic properties of the process and characterize the corresponding invariant measure. This extends…
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…
As two crucial tools characterizing regularity properties of stochastic systems, the log-Harnack inequality and Bismut formula have been intensively studied for distribution dependent (McKean-Vlasov) SDEs. However, due to technical…
Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift $b$ to some reference drift $b_0$: At prescribed significance, we simultaneously identify those regions where violation from…
We study the long time statistics of a two-dimensional Hamiltonian system in the presence of Gaussian white noise. While the original dynamics is known to exhibit finite time explosion, we demonstrate that under the impact of the stochastic…
The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly…
By starting from the stochastic Schr\"odinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white…
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…
First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic results on $\mR^d$ require that the process is irreducible, we weaken it to some weak form of irreducibility in this article. The main method used in this article…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…
This paper investigates how the structure of the underlying graph influences the behavior of stochastic partial differential equations (SPDEs) on finite tree graphs, where each edge is driven by space-time white noise. We first introduce a…
This work focuses on the regularization by nonlinear noise for a class of partial differential equations that may only have local solutions. In particular, we obtain the global existence, uniqueness and the Feller property for stochastic 3D…
We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the…
We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…