A class of limit theorems for singular diffusions

Class of Limit Theorems for Singular Diffusions

Stability in Distribution for a Class of Singular Diffusions

Central Limit Theorem for a Class of Relativistic Diffusions

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and Hänggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for ...

Mean Field Limit for Disordered Diffusions with Singular Interactions

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in R in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice Z, and the interaction between two diffusions is attenuated by a spatial weight that depends on ...

Spectral analysis of a family of symmetric, scale- invariant diffusions with singular coefficients and associated limit theorems

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving limit theorems resulting in non-Gaussian, scale-invariant diffusions. We apply the generalized characteristic functions in combination with a martingale const...