Sharp estimates for the convergence of the density of the Euler scheme in small time.
Smooth measures, the Malliavin calculus and approximations in infinitedimensional spaces
Smoothness of the law of the supremum of the fractional Brownian motion.
Some Fine Properties of BV Functions on Wiener Spaces
In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.
Some fine properties of sets with finite perimeter in Wiener spaces
In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...
SPDEs with pseudodifferential generators: the existence of a density
We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain , and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point is absolutely continuous with respect to the Lebesgue measure.
Splitting the conservation process into creation and annihilation parts
The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Stochastic analysis of Bernoulli processes.
Stochastic calculus and degenerate boundary value problems
Consider the boundary value problem (L.P): in , on where is written as , and is a general Venttsel’s condition (including the oblique derivative condition). We prove existence, uniqueness and smoothness of the solution of (L.P) under the Hörmander’s condition on the Lie brackets of the vector fields (), for regular open sets with a non-characteristic boundary.Our study lies on the stochastic representation of and uses the stochastic calculus of variations for the -diffusion process...
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.