- 期刊
Large Deviations for the Maximum of the Absolute Value of Partial Sums of Independent Random Variables Sequence With Finite Moment Generating Function
摘要
Purpose: Let {ξ_i: i ≥ 1} be a sequence of independent and identically distributed (i.i.d.) random variables. In this paper we investigate the large deviations for the maximum of the absolute value of partial sums S_n: =Σ_i^n =_1ξ_i. Approach: The sample path large deviations and the contraction principle. Findings: We obtain that the sequence {1/n max_(1≤k≤n)|S_k|: n ≥ 1} satisfies the large deviation principle with a good rate function. Value: We can obtain the asymptotic estimation for probability P(1/n max_(1≤k≤n)|S_k| ∈ B) for any Borel measurable set B in R.
延伸閱讀
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