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Inequalities and principles of large deviations for the trajectories of processes with independent increments

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Abstract

We consider a homogeneous process S(t) on [0,∞) with independent increments, establish the local and ordinary large deviation principles for the trajectories of the processes \(s_T (t): = \tfrac{1} {T}S(tT) \), t ∈ [0, 1], as T → ∞, and obtain a series of inequalities for the distributions of the trajectories of S(t).

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Correspondence to A. A. Borovkov.

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Original Russian Text Copyright © 2013 Borovkov A.A. and Mogul’skiĭ A.A.

The authors were supported by the Russian Foundation for Basic Research (Grant 11-01-00285) and the Ministry for Education of the Russian Federation (Grant RNP.2.1.1.346).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 2, pp. 286–297, March–April, 2013.

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Borovkov, A.A., Mogul’skiĭ, A.A. Inequalities and principles of large deviations for the trajectories of processes with independent increments. Sib Math J 54, 217–226 (2013). https://doi.org/10.1134/S0037446613020055

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  • DOI: https://doi.org/10.1134/S0037446613020055

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