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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 122–150 (Mi tvp304)  

This article is cited in 10 scientific papers (total in 10 papers)

The large deviation principle for stochastic processes. II

M. A. Arcones

State University of New York, Department of Mathematical Sciences

Abstract: We discuss the large deviation principle of stochastic processes as random elements of $l_{\infty}(T)$. We show that the large deviation principle in $l_{\infty}(T)$ is equivalent to the large deviation principle of the finite dimensional distributions plus an exponential asymptotic equicontinuity condition with respect to a pseudometric which makes $T$ a totally bounded pseudometric space. This result allows us to obtain necessary and sufficient conditions for the large deviation principle of different types of stochastic processes. We discuss the large deviation principle of Gaussian and Poisson processes. As an application, we determine the integrability of the iterated fractional Brownian motion.

Keywords: large deviations, stochastic processes, Gaussian processes, iterated Brownian motion, Poisson process.

DOI: https://doi.org/10.4213/tvp304

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English version:
Theory of Probability and its Applications, 2004, 48:1, 19–44

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Received: 05.04.2001
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Citation: M. A. Arcones, “The large deviation principle for stochastic processes. II”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 122–150; Theory Probab. Appl., 48:1 (2004), 19–44

Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2004
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\pages 19--44
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    This publication is cited in the following articles:
    1. Mason D.M., “A uniform functional law of the logarithm for the local empirical process”, Ann. Probab., 32:2 (2004), 1391–1418  crossref  mathscinet  zmath  isi  scopus
    2. Varron D., “A limited in bandwidth uniformity for the functional limit law of the increments of the empirical process”, Electronic Journal of Statistics, 2 (2008), 1043–1064  crossref  mathscinet  zmath  isi  scopus
    3. Merlevede F., Peligrad M., “Functional moderate deviations for triangular arrays and applications”, Alea-Latin American Journal of Probability and Mathematical Statistics, 5 (2009), 3–20  mathscinet  zmath  isi
    4. Merlevède F., Peligrad M., “Moderate deviations for linear processes generated by martingale-like random variables”, J. Theor. Probab., 23:1 (2010), 277–300  crossref  mathscinet  zmath  isi  scopus
    5. Coiffard C., “Random Fractals Generated by a Local Gaussian Process Indexed by a Class of Functions”, ESAIM-Probability and Statistics, 15 (2011), 249–269  crossref  mathscinet  zmath  isi  scopus
    6. Gao F., Zhao X., “Delta Method in Large Deviations and Moderate Deviations for Estimators”, Ann Statist, 39:2 (2011), 1211–1240  crossref  mathscinet  zmath  isi  scopus
    7. Theory Probab. Appl., 59:1 (2015), 70–86  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Penda S. Valere Bitseki, Djellout H., Proia F., “Moderate Deviations For the Durbin-Watson Statistic Related To the First-Order Autoregressive Process”, ESAIM-Prob. Stat., 18 (2014), 308–331  crossref  mathscinet  zmath  isi  scopus
    9. M. S. Ermakov, “On conistent hypothesis testing”, J. Math. Sci. (N. Y.), 225:5 (2017), 751–769  mathnet  crossref  mathscinet
    10. Del Moral P., Hu Sh., Wu L., “Moderate Deviations For Interacting Processes”, Stat. Sin., 25:3 (2015), 921–951  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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