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On the distribution of functionals of the subordinator

Author: D. V. Gusak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 51-66
MSC (2010): Primary 60G50; Secondary 60K10
Published electronically: July 24, 2014
MathSciNet review: 3112634
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Abstract | References | Similar Articles | Additional Information

Abstract: The distributions of boundary functionals have been studied by many authors for stochastic processes with independent stationary increments. (See, for example, [1]-[6].) If a process possesses a bounded variation and the drift is nonnegative, then one can obtain (see [4, 5]) the relations determining the distributions of some functionals of the subordinator defined as a stochastic process with independent positive increments; see Chapter III of [3].

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Additional Information

D. V. Gusak
Affiliation: 252601, Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street 3, Kyiv, Ukraine

Keywords: Stochastic processes with stationary independent increments, subordinator, cumulant and potential of stochastic processes
Received by editor(s): December 13, 2011
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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