Open AccessRate of Convergence, Relation Between the Arcsine Law and P(τ≤n) in the Optimal Stopping Problem For S_n/n
Publication year - 2022
Publication title -
european journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 2055-0162
pISSN - 2055-0154
DOI - 10.37745/ejsp.2013/vol10no1pp.1-10
Subject(s) - mathematics , convergence (economics) , combinatorics , rate of convergence , computer science , economics , economic growth , computer network , channel (broadcasting)
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 between1/(2(N+1)) E |X_1 | ∀ Nand (1+ε ) 2/N^(3/4) for arbitrary ε> 0, N>N_ε.