Publications and Preprints

Convergence of Lower Records and Infinite divisiblity
by
Arup Bose, Sreela Gangopadhyay, Anish Sarkar and Arindam Sengupta
We study the properties of sums of lower records from a distribution on $[0, \infty)$ which either is continuous, except possibly at the origin or has support contained in the set of non-negative integers. We find necessary and sufficient condition for the partial sums of lower records to converge almost surely to a proper random variable. Explicit formula for the Laplace transform of the limit is derived. This limit is infinite divisible and we show that all infinitely divisible random variables with continuous Levy measure on $[0, \infty)$ originate as infinite sums of lower records.

isid/ms/2003/09 [fulltext]