Large Deviations for the Maximum of the Absolute Value of Partial Sums of Random Variable Sequences

Xia Wang and Miaomiao Zhang
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Xia Wang: Faculty of Science, College of Statistics and Date Science, Beijing University of Technology, Beijing 100124, China
Miaomiao Zhang: Faculty of Science, College of Statistics and Date Science, Beijing University of Technology, Beijing 100124, China

Mathematics, 2022, vol. 10, issue 5, 1-11

Abstract: Let { ξ i : i ≥ 1 } be a sequence of independent, identically distributed (i.i.d. for short) centered random variables. Let S n = ξ 1 + ⋯ + ξ n denote the partial sums of { ξ i } . We show that sequence { 1 n max 1 ≤ k ≤ n | S k | : n ≥ 1 } satisfies the large deviation principle (LDP, for short) with a good rate function under the assumption that P ( ξ 1 ≥ x ) and P ( ξ 1 ≤ − x ) have the same exponential decrease.

Keywords: large deviation principle; principle of the largest term; maximum of the absolute value of partial sums (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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