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,... Fort∈[0, 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\(\tilde S_n \).
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Schuette, P.H. Large deviations for trajectories of sums of independent random variables. J Theor Probab 7, 3–45 (1994). https://doi.org/10.1007/BF02213359
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DOI: https://doi.org/10.1007/BF02213359