On the product of a random and a real measure
Author:
V. M. Radchenko
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 70 (2005), 161-166
MSC (2000):
Primary 60G57
DOI:
https://doi.org/10.1090/S0094-9000-05-00639-3
Published electronically:
August 12, 2005
MathSciNet review:
2110872
Full-text PDF Free Access
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Abstract: The product of a random measure $X$ and a real measure $Y$ is defined as a random measure on $X\times Y$. We obtain conditions under which the integral of a real function with respect to the product measure equals the iterated integrals of this function.
References
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References
- Y. Mishura and E. Valkeila, An isometric approach to generalized stochastic integrals, J. Theoret. Probab. 13 (2000), 673–693. MR 1785525 (2001k:60075)
- S. Kwapień and W. A. Woycziński, Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, MA, 1992. MR 1167198 (94k:60074)
- V. N. Radchenko, Integrals with respect to general random measures, Proceedings of the Institute of Mathematics of the Academy of Sciences of Ukraine, vol. 27, 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, Uniform integrability for integrals with respect to $L_{0}$-valued measures, Ukrain. Mat. Zh. 43 (1991), no. 9, 1264–1267; English transl. in Ukrainian Math. J. 43 (1991), no. 9, 1178–1180. MR 1149591 (93b:28025)
- Yu. V. Krvavich and Yu. S. Mishura, The differentiability of fractional integrals whose kernels contain fractional Brownian motions, Ukrain. Mat. Zh. 53 (2001), no. 1, 30–40; English transl. in Ukrainian Math. J. 53 (2001), no. 1, 35–47. MR 1834637 (2002d:60046)
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- V. N. Radchenko, On a definition of the integral of a random function, Teor. Veroyatnost. i Primenen. 41 (1996), no. 3, 677–682; English transl. in Theory Probab. Appl. 41 (1996), no. 3, 597–601. MR 1450086 (98f:60002)
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Additional Information
V. M. Radchenko
Affiliation:
Mathematical Institute, University of Jena, 07740 Jena, Germany
Email:
vradchenko@univ.kiev.ua
Keywords:
Random measure,
stochastic integral,
product of measures,
Fubini theorem
Received by editor(s):
June 17, 2003
Published electronically:
August 12, 2005
Additional Notes:
Partially supported by the Alexander von Humboldt Foundation, grant 1074615.
Article copyright:
© Copyright 2005
American Mathematical Society
