Self-interacting diffusions II : convergence in law
Semimartingales in predictable random open sets
Sharp estimates of the Green function of hyperbolic Brownian motion
The main objective of the work is to provide sharp two-sided estimates of the λ-Green function, λ ≥ 0, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
Shrinkage strategies in some multiple multi-factor dynamical systems
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the...
Shrinkage strategies in some multiple multi-factor dynamical systems
In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the...
Singularités des fonctions de Green hypoelliptiques
Smoothness of Itô maps and diffusion processes on path spaces (I)
Some heat operators on
Some remarks on the heat flow for functions and forms.
Speed of the Brownian loop on a manifold
We define the speed of the curved Brownian bridge as a white noise distribution operating on stochastic Chen integrals.
Stochastic calculus and martingales on trees
Stochastic differential inclusions of Langevin type on Riemannian manifolds
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
Stochastic methods and differential geometry
Stochastic parallel transport and connections of
In this paper we prove that there is a bijective correspondence between connections of , the principal bundle of the second order frames of , and stochastic parallel transport in the tangent space of . We construct in a direct geometric way a prolongation of connections without torsion of to connections of . We interpret such prolongation in terms of stochastic calculus.
Stochastic processes and antiderivational equations on non-Archimedean manifolds.
Sur une formule de Bismut