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
MathSciNet review:
3824680
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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