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

Author

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  • Alexander I. Nazarov

    (St. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, 191023 St. Petersburg, Russia
    Saint-Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia)

  • Yakov Yu. Nikitin

    (Saint-Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
    National Research University, Higher School of Economics, Souza Pechatnikov 16, 190008 St. Petersburg, Russia)

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.

Suggested Citation

  • Alexander I. Nazarov & Yakov Yu. Nikitin, 2018. "On Small Deviation Asymptotics In L 2 of Some Mixed Gaussian Processes," Mathematics, MDPI, vol. 6(4), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:55-:d:139793
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    References listed on IDEAS

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    1. El-Nouty, Charles, 2003. "The fractional mixed fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 65(2), pages 111-120, November.
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