A conditional strong large deviation result and a functional central limit theorem for the rate function

2014/11/21 by Anton Bovier, Bovier, Anton, Hannah Mayer +1 · 2 citations
Mathematics · Decision Sciences · #Stochastic processes and statistical mechanics #Probability and Risk Models #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1411.5803

Abstract

We study the large deviation behaviour of S_n=∑_j=1ⁿ W_jZ_j, where (W_j)_{j ∈ \mathbb N} and (Z_j)_{j ∈ \mathbb N} are sequences of real-valued, independent and identically distributed random variables satisfying certain moment conditions, independent of each other. More precisely, we prove a conditional strong large deviation result and describe the fluctuations of the random rate function through a functional central limit theorem.

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