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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Riemann integral of a random function and the parabolic equation with a general stochastic measure


Author: V. Radchenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 185-198
MSC (2000): Primary 60H05, 60H15
Published electronically: March 21, 2014
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Abstract: For a stochastic parabolic equation driven by a general stochastic measure, the weak solution is obtained. The integral of a random function in the equation is considered as a limit in probability of Riemann integral sums. Basic properties of such integrals are studied in this paper.


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Additional Information

V. Radchenko
Affiliation: Department of Mathematical Analysis, Kyiv National Taras Shevchenko University, Kyiv 01601, Ukraine
Email: vradchenko@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2014-00912-6
PII: S 0094-9000(2014)00912-6
Keywords: Stochastic measure, Riemann integral, stochastic parabolic equation, weak solution
Received by editor(s): December 22, 2011
Published electronically: March 21, 2014
Additional Notes: This research was supported by Alexander von Humboldt Foundation, grant no. UKR/1074615. The author wishes to thank Professor M. Zähle for fruitful discussions, and the hospitality of Jena University is gratefully acknowledged
Article copyright: © Copyright 2014 American Mathematical Society