期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2014
卷号：XI
页码：711-735
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We establish a link between the distribution of an exponential functional,I; and the undershoots of a subordinator, which is given in terms of theassociated harmonic potential measure. This allows us to give a necessary andsucient condition in terms of the Levy measure for the exponential functional tobe multiplicative in nitely divisible. We then provide a formula for the momentgenerating functions of log I and logR where R is the so-called remainder randomvariable associated to I. We provide a realization of the remainder random variableR as an in nite product involving independent last position random variables ofthe subordinator. Some properties of harmonic measures are obtained and someexamples are provided.
关键词：Exponential functionals; Harmonic potential; In nite divisibility; Sub-;ordinators; Undershoots.
