Solutions faibles et semi-martingales
Solutions of stochastic differential equations obeying the law of the iterated logarithm, with applications to financial markets.
Solutions statistiques homogènes des systèmes différentiels paraboliques et du système de Navier-Stokes
Solvability of Kolmogorov-Fokker-Planck equations for vectorjump processes and occupation time on hypersurfaces.
Some additional remarks on Fock space stochastic calculus
Some Dirichlet spaces obtained by subordinate reflected diffusions.
In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
Some Distribution-Free Small Samples Methods for Interval Estimation and Hypothesis Testing in Linear Shock Models
Some estimates on exponentials of solutions to stochastic differential equations.
Some examples of holomorphic processes
Some extensions of Ito's formula
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...
Some limit theorems for one type of stochastic integro-differential equations.
Some Markov properties of stochastic differential equations with jumps
Some maximum principles for stochastic equations
Some non-linear s. p. d. e's that are second order in time.
Some properties of exponential integrals of Levy processes and examples.
Some properties of martingale integrals
Some properties of random fields connected with stochastic integrals with respect to strong martingales.
Some properties of superprocesses under a stochastic flow
For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s Lp-theory for linear SPDE.