Related papers: Support theorem for pinned diffusion processes

We prove a support theorem of the type of Stroock-Varadhan for solutions of stochastic variational inequalities.

We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation (SPDE) on the real line with a noise term driven by a cylindrical Wiener process on $L_2 (\mathbb{R})$. The main ingredients of the proof are…

Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given by the image of the Cameron-Martin space under the flow of…

These are lecture notes for a Master 2 course on rough differential equations driven by weak geometric Holder p-rough paths, for any p>2. They provide a short, self-contained and pedagogical account of the theory, with an emphasis on flows.…

In this paper, we establish the Stroock-Varadhan type support theorems for stochastic differential equations (SDEs) under Lyapunov conditions, which significantly improve the existing results in the literature where the coefficients of the…

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

Since T. Lyons invented rough path theory, one of its most successful applications is a new proof of Freidlin-Wentzell's large deviation principle for diffusion processes. In this paper we extend this method to the case of pinned diffusion…

We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…

Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…

We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nash, Moser, Aronson extend to this setting. It was then…

In this paper, we consider a Stochastic Delay Differential Equation with constant delay $r>0$ and, under the same conditions on the coefficients needed to ensure the smoothness of the density plus an ellipticity condition on the diffusion…

In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard…

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H in (1/3,1/2). More precisely, we resort to the Kac-Stroock type…

We derive a generalization of the Wiener-Khinchin theorem for nonstationary processes by introducing a time-dependent spectral density that is related to the time-averaged power. We use the nonstationary theorem to investigate aging…

We prove a representation for the support of McKean Vlasov Equations. To do so, we construct functional quantizations for the law of Brownian motion as a measure over the (non-reflexive) Banach space of H\"older continuous paths. By solving…

Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…

We consider a nonlinear Fokker-Planck equation driven by a deterministic rough path which describes the conditional probability of a McKean-Vlasov diffusion with "common" noise. To study the equation we build a self-contained framework of…

We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential equations, solutions of which require renormalization and…

We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problems as well as some…

We consider a system of stochastic differential equations driven by a standard n-dimensional Brownian motion where the drift coefficient satisfies a Novikov-type condition while the diffusion coefficient is the identity matrix. We define a…