Brownian sheet and capacity. (English) Zbl 0962.60066

The paper deals with the Brownian sheet, a temporally inhomogeneous, multiparameter, centered continuous Gaussian process. One of the goals of the paper is to provide an elementary proof of a result of S. Song [Séminaire de probabilités XXVII. Lect. Notes Math. 1557, 276-301 (1993; Zbl 0786.60105)] giving an explicit capacity estimate for the hitting probabilities of the Brownian sheet. As applications, the escape rates of the Brownian sheet are determined; a local intersection equivalence between the Brownian sheet and the additive Brownian motion is proved; and results concerning quasi-sure properties in Wiener space are proved.


60J45 Probabilistic potential theory
60G60 Random fields
31C15 Potentials and capacities on other spaces
60H07 Stochastic calculus of variations and the Malliavin calculus
60G17 Sample path properties
47D07 Markov semigroups and applications to diffusion processes


Zbl 0786.60105
Full Text: DOI


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