Convergence of lower records and infinite divisibility

Bose, Arup ; Gangopadhyay, Sreela ; Sarkar, Anish ; Sengupta, Arindam (2003) Convergence of lower records and infinite divisibility Journal of Applied Probability, 40 (4). pp. 865-880. ISSN 0021-9002

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Related URL: http://dx.doi.org/10.1239/jap/1067436087

Abstract

We study the properties of sums of lower records from a distribution on [0,8) which is either continuous, except possibly at the origin, or has support contained in the set of nonnegative integers. We find a necessary and sufficient condition for the partial sums of lower records to converge almost surely to a proper random variable. An explicit formula for the Laplace transform of the limit is derived. This limit is infinitely divisible and we show that all infinitely divisible random variables with continuous Levy measure on [0,8) originate as infinite sums of lower records.

Item Type:Article
Source:Copyright of this article belongs to Applied Probability Trust.
ID Code:93946
Deposited On:30 Jun 2012 08:07
Last Modified:30 Jun 2012 08:07

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