Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables
| Autor: | Dianliang Deng |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2009 (2009) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/2009/253750 |
| Popis: | Let {X,Xn¯;n¯∈Z+d} be a sequence of i.i.d. real-valued random variables, and Sn¯=∑k¯≤n¯Xk¯, n¯∈Z+d. Convergence rates of moderate deviations are derived; that is, the rates of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of the series ∑n¯b(n¯)ψ2(a(n¯))P{|Sn¯|≥a(n¯)ϕ(a(n¯))}, where a(n¯)=n11/α1⋯nd1/αd, b(n¯)=n1β1⋯ndβd, ϕ and ψ are taken from a broad class of functions. These results generalize and improve some results of Li et al. (1992) and some previous work of Gut (1980). |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|