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Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza (2012)

ESAIM: Probability and Statistics

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

Gérard Ben Arous, Mihai Gradinaru (1996)

Annales mathématiques Blaise Pascal

Smoothness of Itô maps and diffusion processes on path spaces (I)

Xiang-Dong Li, Terry J. Lyons (2006)

Annales scientifiques de l'École Normale Supérieure

Some heat operators on $ℙ (ℝ^{d})$

H. Airault, P. Malliavin (1996)

Annales mathématiques Blaise Pascal

Some remarks on the heat flow for functions and forms.

Thalmaier, Anton (1998)

Electronic Communications in Probability [electronic only]

Speed of the Brownian loop on a manifold

Rémi Léandre (2006)

Banach Center Publications

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

Jean Picard (2005)

Annales de l'I.H.P. Probabilités et statistiques

Stochastic differential inclusions of Langevin type on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovskiĭ (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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

K. David Elworthy (1980/1981)

Séminaire Bourbaki

Stochastic parallel transport and connections of $H^{2} M$

Pedro Catuogno (1999)

Archivum Mathematicum

In this paper we prove that there is a bijective correspondence between connections of $H^{2} M$ , the principal bundle of the second order frames of $M$ , and stochastic parallel transport in the tangent space of $M$ . We construct in a direct geometric way a prolongation of connections without torsion of $M$ to connections of $H^{2} M$ . We interpret such prolongation in terms of stochastic calculus.