Tu, Ly Hoang and Hanoi, Vietnam (2022) Rate of Convergence, Relation Between the Arcsine Law and P(τ≤n) in the Optimal Stopping Problem For S_n/n,. European Journal of Statistics and Probability, 10 (1). pp. 1-10. ISSN 2055-0154(Print), 2055-0162(Online)
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Abstract
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 .
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Optimal stopping time, backward induction, the arcsine law, the Fatou – Lebesgue`s theorem. Symmetric Bernoulliˋs distribution. Generating function, AMS (2000) Subject classification. |
| Subjects: | Q Science > QA Mathematics |
| Depositing User: | Professor Mark T. Owen |
| Date Deposited: | 11 Apr 2022 16:32 |
| Last Modified: | 11 Apr 2022 16:32 |
| URI: | https://tudr.org/id/eprint/330 |
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