Small deviation probabilities of some stochastic processes

Aurzada, Frank GND

This thesis discusses the small deviation problem -- also called small ball or lower tail probability problem -- for certain types of stochastic processes. In particular, weighted sequences of independent random variables in lp are considered. Furthermore, the connection between small deviations and entropy numbers in the case of Gaussian and symmetric stable processes are investigated. The results are applied to concrete sequences of random variables, random Fourier series, and stable convolutions.

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Aurzada, Frank: Small deviation probabilities of some stochastic processes. 2006.

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