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Large deviations for trajectories of sums of independent random variables

Authors:	Paul H Schuette

Institution:	(1) Department of Mathematics, Georgia College, 31061 Milledgeville, Georgia

Abstract:	Given a sequence of independent, but not necessarily identically distributed random variables,Y _i, letS _k denote thekth partial sum. Define a function $\tilde S:0,\infty ) \to \mathbb{R}$ by taking $\tilde S(t)$ to be the piecewise linear interpolant of the points (k, S _k), evaluated att, whereS ₀=0, andk=0, 1, 2,... Fort0, 1], let $\tilde S_n (t)\mathop = \limits^{def} \tilde S(nt)$ . The $\tilde S_n$ are called trajectories. With regularity and moment conditions on theY _i, a large deviation principle is proved for the $\tilde S_n$ .

Keywords:	Large deviations trajectories Gä rtner-Ellis theorems random walk
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