Stochastic calculus and initial value analysis on the one dimensional diffusions.
Stochastic Calculus on One-dimensional Diffusions
Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter
Stochastic integral representation of the modulus of Brownian local time and a central limit theorem.
Stochastic integration with respect to fractional brownian motion
Stochastic integration with respect to Volterra processes
Stochastic partial differential equations with Dirichlet white-noise boundary conditions
Stochastic Poisson-Sigma model
We produce a stochastic regularization of the Poisson-Sigma model of Cattaneo-Felder, which is an analogue regularization of Klauder’s stochastic regularization of the hamiltonian path integral [23] in field theory. We perform also semi-classical limits.
Strict positivity of the solution to a 2-dimensional spatially homogeneous Boltzmann equation without cutoff
Strong innovation and its applications to information diffusion modelling in finance.
Sur certaines relations entre les intégrales trajectorielles et l'opérateur de translation et son dual dans l'espace de Poisson canonique.
We study the relationship between the translation operator, its dual and the pathwise integral on the Poisson space with weak conditions on the processes.
Sur le théorème de l'indice des familles
SURE shrinkage of gaussian paths and signal identification
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
SURE shrinkage of Gaussian paths and signal identification*
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
The abstract Riemannian path space.
The fBm Itô's formula through analytic continuation.
The partial Malliavin calculus
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space.
Time reversal for drifted fractional Brownian motion with Hurst index .
Transportation inequalities for stochastic differential equations of pure jumps
For stochastic differential equations of pure jumps, though the Poincaré inequality does not hold in general, we show that W1H transportation inequalities hold for its invariant probability measure and for its process-level law on right continuous paths space in the L1-metric or in uniform metrics, under the dissipative condition. Several applications to concentration inequalities are given.