Laplace approximations for sums of independent random vectors期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Laplace approximations for sums of independent random vectors

Authors:	E. Bolthausen

Affiliation:	(1) Fachbereich Mathematik, Technische Universität Berlin, Straß des 17. Juni 135, 1000 Berlin 12

Abstract:	Summary LetX_i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of $Z_n = Eleft( {exp left( {nphi left( {sumlimits_{i = 1}^n {{{X_i } mathord{left/ {vphantom {{X_i } n}} right. kern-nulldelimiterspace} n}} } right)} right)} right)$ is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums $sumlimits_{i = 1}^n {X_i }$ under the law transformed by the density exp ${{left( {nphi left( {sumlimits_{i = 1}^n {{{X_i } mathord{left/ {vphantom {{X_i } n}} right. kern-nulldelimiterspace} n}} } right)} right)} mathord{left/ {vphantom {{left( {nphi left( {sumlimits_{i = 1}^n {{{X_i } mathord{left/ {vphantom {{X_i } n}} right. kern-nulldelimiterspace} n}} } right)} right)} {Z_n }}} right. kern-nulldelimiterspace} {Z_n }}$ .

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