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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/253750 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551324014608384 |
|---|---|
| author | Dianliang Deng |
| author_facet | Dianliang Deng |
| author_sort | Dianliang Deng |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-7657e79739b74f2193cab13461415048 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7657e79739b74f2193cab134614150482025-02-03T06:01:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/253750253750Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random VariablesDianliang Deng0Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2, CanadaLet {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).http://dx.doi.org/10.1155/2009/253750 |
| spellingShingle | Dianliang Deng Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables International Journal of Mathematics and Mathematical Sciences |
| title | Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables |
| title_full | Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables |
| title_fullStr | Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables |
| title_full_unstemmed | Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables |
| title_short | Convergence Rates for Probabilities of Moderate Deviations for Multidimensionally Indexed Random Variables |
| title_sort | convergence rates for probabilities of moderate deviations for multidimensionally indexed random variables |
| url | http://dx.doi.org/10.1155/2009/253750 |
| work_keys_str_mv | AT dianliangdeng convergenceratesforprobabilitiesofmoderatedeviationsformultidimensionallyindexedrandomvariables |