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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 

 

Parameter-dependent integrals with respect to general random measures


Author: V. M. Radchenko
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 161-165
MSC (2000): Primary 60G57
Published electronically: January 25, 2008
MathSciNet review: 2321189
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Abstract: We study integrals of real functions considered with respect to general random measures. The integrals are assumed to depend on a parameter. We obtain sufficient conditions for the existence of a continuous version of random functions and sufficient conditions such that a random measure generated by increments of these random functions exists.


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Additional Information

V. M. Radchenko
Affiliation: Department of Mathematical Analysis, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: vradchenko@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-08-00722-9
Keywords: Random measure, stochastic integral dependent on a parameter, continuity of sample paths of a stochastic process
Received by editor(s): January 20, 2006
Published electronically: January 25, 2008
Article copyright: © Copyright 2008 American Mathematical Society