Parameter-dependent integrals with respect to general random measures
Author:
V. M. Radchenko
Translated by:
O. I. Klesov
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
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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.
References
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References
- 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)
- S. Kwapień and W. A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, 1992. MR 1167198 (94k:60074)
- 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)
- 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)
- 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)
- 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
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
