arXiv subjects

S. Tindel

Publications and source records attributed to S. Tindel.

4 recordsLinked to original sources

arXiv2016

Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter $H$. In the one-dimensional case with additive noise, our study encompasses all parameters $H\in(0,1)$, while the multidimensional case is restricted to the case $H>1/2$. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.

math.PR↗

arXiv2009

Non-linear Rough Heat Equations

This article is devoted to define and solve an evolution equation of the form $dy_t=Δy_t dt+ dX_t(y_t)$, where $Δ$ stands for the Laplace operator on a space of the form $L^p(\mathbb{R}^n)$, and $X$ is a finite dimensional noisy nonlinearity whose typical form is given by $X_t(φ)=\sum_{i=1}^N x^{i}_t f_i(φ)$, where each $x=(x^{(1)},...,x^{(N)})$ is a $γ$-Hölder function generating a rough path and each $f_i$ is a smooth enough function defined on $L^p(\mathbb{R}^n)$. The generalization of the usual rough path theory allowing to cope with such kind of systems is carefully constructed.

math.PR↗

arXiv2002

The p-spin interaction model with external field

This paper is devoted to a detailed study of a p-spins interaction model with external field, including some sharp bounds on the speed of self averaging of the overlap as well as a central limit theorem for its fluctuations, the thermodynamical limit for the free energy and the definition of an Almeida-Thouless type line. Those results show that the external field dominates the tendency to disorder induced by the increasing level of interaction between spins, and our system will share many of its features with the SK model, which is certainly not the case when the external magnetic field vanishes.

math.PR↗

arXiv2002

Higher order expansions for the overlap of the SK model

In this note, the Sherrington Kirkpatrick model of interacting spins is under consideration. In the high temperature region, we give an asymptotic expansion for the expected value of some genereral polynomial of the overlap of the system when the size $N$ grows to infinity. Some of the coefficients obtained are shown to be vanishing, while the procedure to get the nontrivial ones has to be performed by a computer program, due to the great amount of computation involved.

math.PR↗