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Chaos expansions and local times.

David Nualart, Josep Vives (1992)

Publicacions Matemàtiques

In this note we prove that the Local Time at zero for a multiparametric Wiener process belongs to the Sobolev space Dk - 1/2 - ε,2 for any ε > 0. We do this computing its Wiener chaos expansion. We see also that this expansion converges almost surely. Finally, using the same technique we prove similar results for a renormalized Local Time for the autointersections of a planar Brownian motion.

Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud (2001)

ESAIM: Probability and Statistics

In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

Chernoff and Berry–Esséen inequalities for Markov processes

Pascal Lezaud (2010)

ESAIM: Probability and Statistics

In this paper, we develop bounds on the distribution function of the empirical mean for general ergodic Markov processes having a spectral gap. Our approach is based on the perturbation theory for linear operators, following the technique introduced by Gillman.

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