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Sharp estimates of the Green function of hyperbolic Brownian motion

Kamil Bogus, Tomasz Byczkowski, Jacek Małecki (2015)

Studia Mathematica

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

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...

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...

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 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 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.

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