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

DOI:
https://doi.org/10.1090/S0094-9000-08-00722-9

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.

**1.**J. Memin, Yu. Mishura, and E. Valkeila,*Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion*, Statist. Probab. Lett.**57**(2001), no. 2, 197-206. MR**1822771 (2002b:60096)****2.**S. Kwapień and W. A. Woyczyński,*Random Series and Stochastic Integrals: Single and Multiple*, Birkhäuser, Boston, 1992. MR**1167198 (94k:60074)****3.**V. N. Radchenko,*Integrals with respect to general random measures*, Proceedings of the Institute of Mathematics, National Academy of Sciences of Ukraine, vol. 27, Institute of Mathematics, Kiev, 1999. (Russian)**4.**V. N. Radchenko,*Integrals with respect to random measures and random linear functionals*, Teor. Veroyatnost. i Primenen.**36**(1991), no. 3, 594-596; English transl. in Theory Probab. Appl.**36**(1991), no. 3, 621-623. MR**1141138 (93e:60093)****5.**V. N. Radchenko,*On the product of random and real measures*, Teor. Imovir. Mat. Stat.**70**(2004), 144-148; English transl. in Theory Probab. Math. Statist.**70**(2005), 161-166. MR**2110872 (2005h:60146)****6.**I. P. Natanson,*Theory of Functions of a Real Variable*, Third edition, ``Nauka'', Moscow, 1974; English transl., Frederick Ungar Publishing, New York, 1967. MR**0354979 (50:7456)**

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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