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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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