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Small ball probabilities for Gaussian Markov processes under the Lp-norm

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  • V. Li, Wenbo

Abstract

Let {X(t); 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a real-valued continuous Gaussian Markov process with mean zero and covariance [sigma](s,t)=EX(s)X(t)[not equal to]0 for 0 0, H>0 and G/H nondecreasing on the interval (0,1). We show that for the Lp-norm on C[0,1], 1[less-than-or-equals, slant]p[less-than-or-equals, slant][infinity]and its various extensions.

Suggested Citation

  • V. Li, Wenbo, 2001. "Small ball probabilities for Gaussian Markov processes under the Lp-norm," Stochastic Processes and their Applications, Elsevier, vol. 92(1), pages 87-102, March.
    • Handle: RePEc:eee:spapps:v:92:y:2001:i:1:p:87-102
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    Cited by:

    1. S. Dereich & F. Fehringer & A. Matoussi & M. Scheutzow, 2003. "On the Link Between Small Ball Probabilities and the Quantization Problem for Gaussian Measures on Banach Spaces," Journal of Theoretical Probability, Springer, vol. 16(1), pages 249-265, January.

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