This article is cited in 19 papers

The large deviation principle for stochastic processes. I

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.

Received: 05.04.2001

Language: English

DOI: 10.4213/tvp3777

 English version: Theory of Probability and its Applications, 2003, 47:4, 567–583

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