Abstract
Our main goal is to study the behavior of the tail probabilities \({\mathbf{P}}(V^2<r)\) as \(r\rightarrow 0\), where \(V^2\) is defined by the following double sum
where \( \{\xi _{ij}\} \) are independent standard normal random variables, and b and \({\delta }\) are constants: \(b>-1\) and \(\delta >-1\).
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Acknowledgements
The author is indebted to professors M. A. Lifshits, Ya. Yu. Nikitin and A. I. Nazarov (Saint Petersburg State University) for helpful discussions, and an anonymous referee for valuable comments.
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The research was supported by Russian Foundation for Basic Research (Grant 16-01-00367).
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Rozovsky, L.V. Small Ball Probabilities for Certain Gaussian Random Fields. J Theor Probab 32, 934–949 (2019). https://doi.org/10.1007/s10959-017-0805-x
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DOI: https://doi.org/10.1007/s10959-017-0805-x