This article is cited in 10 papers

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

A. A. Borovkov, A. A. Mogul'skiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We consider a homogeneous process $S(t)$ on $[0,\infty)$ with independent increments, establish the local and ordinary large deviation principles for the trajectories of the processes $s_T(t):=\frac1TS(tT)$, $t\in[0,1]$, as $T\to\infty$, and obtain a series of inequalities for the distributions of the trajectories of $S(t)$.

Keywords: process with independent increments, Cramer's condition, function of deviations, large deviation principle (LDP), local large deviation principle (local LDP), Chebyshev-type inequality, convex set.

UDC: 519.21

Received: 15.06.2012

 English version: Siberian Mathematical Journal, 2013, 54:2, 217–226

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