- 期刊
Moderate Deviations for Maximum of Partial Sums of Independent Identically Distributed Random Variables
摘要
Purpose: In this paper we study the moderate deviations for maximum of partial sums S_n = X_1 + X_2 + ... + X_n of independent identically distributed random variables with zero mean value. Approach: Chernoff's bound and Cramér's theorem. Findings: We prove that the sequence (The equation is abbreviated) satisfies the moderate deviation principle with speed n_β where β ∈ (0, 1) and S_n is the partial sums. Practical implications: Through our result, we can estimate the probability P((The equation is abbreviated) some fixed value) when n is enough large. Value: We can deal with the asymptotic estimation for probability P((The equation is abbreviated) some fixed value) although we do not know the distribution of these random variables.
延伸閱讀
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