On Small Deviation Asymptotics In L 2 of Some Mixed Gaussian Processes

Alexander I. Nazarov and Yakov Yu. Nikitin
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Alexander I. Nazarov: St. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
Yakov Yu. Nikitin: Saint-Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia

Mathematics, 2018, vol. 6, issue 4, 1-9

Abstract: We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen–Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

Keywords: mixed Gaussian process; small deviations; exact asymptotics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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