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Limit laws for sums of products of exponentials of<Emphasis Type="Italic">iid</Emphasis> random variables

Authors:	Email author" target="_blank">Michael?Cranston Email author Stanislav?Molchanov

Institution:	(1) Department of Mathematics, University of California, Irvine 103 MSTB, 92697-3875 Irvine, CA, USA;(2) Department of Mathematics, University of North Carolina-Charlotte, 376 Fretwell Bldg., 28223-0001 Charlotte, NC, USA

Abstract:	We study limit laws for sums of products of exponentials of nonnegative,iid random variables {V _ij}, namely $\sum _{i = 1}^{N(n)} e^{\beta \sum _{j = 1}^n V_{ij} }$ . Under a Cramér type condition,Ee ^sV _ij ]<∞ for somes>0, a weak law of large numbers, central limit theorem, and convergence to stable laws is established for appropriate rates of growth ofN(n) and proper normalizations and scalings. Research of authors supported by grants from NSF.

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