Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables
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 cond...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/253750 |
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| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |