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Large deviations for subordinated Brownian motion and applications

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  • Gajda, Janusz
  • Magdziarz, Marcin

Abstract

This paper concerns the problem of large deviation for the subordinated process ZH(t)=WH(T(t)). The process WH={WH(t),t∈R} is the fractional Brownian motion with Hurst index H∈(0,1) taking values in R. T={T(t),t≥0} is the inverse α-stable subordinator. In this paper we extend the results obtained in M.M. Meerschaert et al. (2008) to the whole range of parameter α∈(0,1).

Suggested Citation

  • Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.
  • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:149-156
    DOI: 10.1016/j.spl.2014.02.003
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    References listed on IDEAS

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    1. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    2. Bañuelos, Rodrigo & DeBlassie, Dante, 2006. "The exit distribution for iterated Brownian motion in cones," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 36-69, January.
    3. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 1995. "Global Strassen-type theorems for iterated Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 321-341, October.
    4. Nane, Erkan, 2008. "Isoperimetric-type inequalities for iterated Brownian motion in," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 90-95, January.
    5. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.
    6. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
    7. Nane, Erkan, 2006. "Iterated Brownian motion in bounded domains in," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 905-916, June.
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    Cited by:

    1. Gajda, J. & Wyłomańska, A. & Kantz, H. & Chechkin, A.V. & Sikora, G., 2018. "Large deviations of time-averaged statistics for Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 47-55.

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