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Theory of Probability and Mathematical Statistics

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On the governing equations for Poisson and Skellam processes time-changed by inverse subordinators


Authors: K. V. Buchak and L. M. Sakhno
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 91-104
MSC (2010): Primary 60G50, 60G51, 60G55
DOI: https://doi.org/10.1090/tpms/1064
Published electronically: August 19, 2019
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Abstract: In the paper we present the governing equations for marginal distributions of Poisson and Skellam processes time-changed by inverse subordinators. The equations are given in terms of convolution-type derivatives.


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Additional Information

K. V. Buchak
Affiliation: Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601, Kyiv, Ukraine
Email: kristina.kobilich@gmail.com

L. M. Sakhno
Affiliation: Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601, Kyiv, Ukraine
Email: lms@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/1064
Keywords: Poisson process, Skellam process, time-change, inverse subordinator, governing equation, convolution-type derivatives
Received by editor(s): January 25, 2018
Published electronically: August 19, 2019
Article copyright: © Copyright 2019 American Mathematical Society