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Parameter-dependent integrals with respect to general random measures
Author(s):
V.
M.
Radchenko
Translated by:
O. I. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
161-165.
MSC (2000):
Primary 60G57
Posted:
January 25, 2008
MathSciNet review:
2321189
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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.
References:
-
- 1.
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- 2.
- S. Kwapień and W. A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, 1992. MR 1167198 (94k:60074)
- 3.
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- 4.
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- 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)
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- 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:
10.1090/S0094-9000-08-00722-9
PII:
S 0094-9000(08)00722-9
Keywords:
Random measure,
stochastic integral dependent on a parameter,
continuity of sample paths of a stochastic process
Received by editor(s):
20/JAN/2006
Posted:
January 25, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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