Properties of integrals with respect to a general stochastic measure in a stochastic heat equation
Author:
V. M. Radchenko
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal:
Theor. Probability and Math. Statist. 82 (2011), 103-114
MSC (2010):
Primary 60G57, 60H15, 60H05
DOI:
https://doi.org/10.1090/S0094-9000-2011-00830-7
Published electronically:
August 4, 2011
MathSciNet review:
2790486
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove a theorem on the continuity with respect to a parameter and an analogue of Fubini's theorem for integrals with respect to a general stochastic measure defined on Borel subsets of . These results are applied to study the stochastic heat equation considered in a mild as well as in a weak form.
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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 2, Kiev 03127, Ukraine
Email:
vradchenko@univ.kiev.ua
DOI:
https://doi.org/10.1090/S0094-9000-2011-00830-7
Keywords:
Random measure,
stochastic integral,
stochastic Fubini theorem,
stochastic convolution
Received by editor(s):
October 5, 2009
Published electronically:
August 4, 2011
Additional Notes:
The research is supported by the Swedish Institute, grant SI-01424/2007
Article copyright:
© Copyright 2011
American Mathematical Society