arXiv subjects
Publications and source records attributed to Samy Tindel.
In this note we show how to generalize the stochastic calculus method introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] for two models of spin glasses, namely, the SK model with external field and the perceptron model. This method allows to derive quite easily some fluctuation results for the free energy in those two cases.
In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical theory and apply to a class of branching and genealogical path-particle models arising in nonlinear filtering literature as well as in statistical physics and biology.
In this note, we study the non-linear evolution problem $dY_t = -A Y_t dt + B(Y_t) dX_t$, where $X$ is a $γ$-Hölder continuous function of the time parameter, with values in a distribution space, and $-A$ the generator of an analytical semigroup. Then, we will give some sharp conditions on $X$ in order to solve the above equation in a function space, first in the linear case (for any value of $γ$ in $(0,1)$), and then when $B$ satisfies some Lipschitz type conditions (for $γ>1/2$). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type.