Displaying similar documents to “Asymptotics for open-loop window flow control.”

Shao's theorem on the maximum of standardized random walk increments for multidimensional arrays

Zakhar Kabluchko, Axel Munk (2009)

ESAIM: Probability and Statistics

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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...

Regularity of irregularities on a brownian path

Samuel James Taylor (1974)

Annales de l'institut Fourier

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On a standard Brownian motion path there are points where the local behaviour is different from the pattern which occurs at a fixed t 0 with probability 1. This paper is a survey of recent results which quantity the extent of the irregularities and show that the exceptional points themselves occur in an extremely regular manner.