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Rate of Convergence, Relation Between the Arcsine Law and P(τ≤n) in the Optimal Stopping Problem For S_n/n
2022
European journal of statistics and probability
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We establish the relation between the arcsine law and P(τ ≤n), and we prove that 〖Sup〗_(t≤N) E S_t/t→ 〖Sup〗_(t≤∞) E S_t/t as N →∞ and the rate of convergence belongs between 1/(2(N+1)) E |X_1 | ∀ N and (1+ε ) 2/N^(3/4) for arbitrary ε> 0, N>N_ε .
doi:10.37745/ejsp.2013/vol10no1pp.1-10
fatcat:frskk3dmard2xf2rg6r4gcmwde