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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
Journal:
Theor. Probability and Math. Statist. 87 (2013), 185-198
MSC (2000):
Primary 60H05, 60H15
DOI:
https://doi.org/10.1090/S0094-9000-2014-00912-6
Published electronically:
March 21, 2014
MathSciNet review:
3241455
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
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. ZÀhle for fruitful discussions, and the hospitality of Jena University is gratefully acknowledged
Article copyright:
© Copyright 2014
American Mathematical Society