Bibliographic Details
| Title: |
Note on Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of I.I.D.: Random Variables under Sublinear Expectations. |
| Authors: |
Xu, Mingzhou1 (AUTHOR), Cheng, Kun1 (AUTHOR) |
| Superior Title: |
Discrete Dynamics in Nature & Society. 9/16/2022, p1-15. 15p. |
| Subject Terms: |
*LOGARITHMS, *INFINITE series (Mathematics), *RANDOM variables |
| Abstract: |
Let X , X n , n ≥ 1 be a sequence of independent, identically distributed random variables under sublinear expectations with C V X 2 < ∞ , lim c ⟶ ∞ E X 2 − c + = 0 , and E ˘ X = E ˘ − X = 0. Write S 0 = 0 , S n = ∑ k = 1 n X n , and M n = max 0 ≤ k ≤ n S k , n ≥ 1. For d > 0 and a n = o log log n − d , we obtain the exact rates in the law of iterated logarithm of a kind of weighted infinite series of C V M n − ε + a n σ ¯ n log log n d + as ε ↓ 0. [ABSTRACT FROM AUTHOR] |
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