Small Deviations for Gaussian Markov Processes Under the Sup-Norm

Wenbo V. Li ()
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Wenbo V. Li: University of Delaware

Journal of Theoretical Probability, 1999, vol. 12, issue 4, 971-984

Abstract: Abstract Let {X(t); 0≤t≤1} be a real-valued continuous Gaussian Markov process with mean zero and covariance σ(s, t) = EX(s) X(t) ≠ 0 for 0 0, H>0 and G/H nondecreasing on the interval (0, 1). We show that $$\mathop {\lim }\limits_{\varepsilon \to 0} \varepsilon ^2 \log P({\text{ }}\mathop {\sup }\limits_{0

Keywords: Small ball problem; Gaussian Markov processes; Brownian motion; weighted norms (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021771503265

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