Small deviations in $L_2$-norm for Gaussian dependent sequences

Small Deviations for Gaussian Markov Processes Under the Sup-Norm

\. INTRODUCTION Let {X(t); 0 < t < 1} be a real-valued mean-zero Gaussian process, and let "||.||" be a semi-norm on the space of real functions on [0, 1]. The so called "small ball estimates" or "small deviation estimates" refer to the asymptotic behavior of This type of problem is quite delicate, and the asymptotic decay rate in (1.1), up to a constant, depends heavily on the process X(t) and...

Small Deviations of Smooth Stationary Gaussian Processes

We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy method due to Kuelbs, Li, and Linde as well as on classical results about the entropy of classes of analytic functions. They also involve Tsirelson’s upper b...

Small deviations for a family of smooth Gaussian processes

We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling properties as standard Brownian motion and plays an important role in the study of zeros of random polynomials. Our estimates are based on several approaches. The precise result for the L2-norm is obtained by an appropriate modificatio...

Small Deviations for SomeMulti - Parameter Gaussian Pro essesbyDavid

Small Deviations of Gaussian Random Fields in Lq–Spaces

We investigate small deviation properties of Gaussian random fields in the space Lq(R N , μ) where μ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby “thin” measures μ, i.e., those which are singular with respect to the N–dimensional Lebesgue measure; the so–called self–similar measures providing a class of typical examples. For a large class of random fi...