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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity of solutions to stochastic Volterra equations with infinite delay


Authors: Anna Karczewska and Carlos Lizama
Journal: Proc. Amer. Math. Soc. 135 (2007), 531-540
MSC (2000): Primary 60H20; Secondary 60H05, 45D05.
Published electronically: August 2, 2006
MathSciNet review: 2255300
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Abstract: In this article we give necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a $ d$-dimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used. The work applies to both the stochastic heat and wave equations.


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Additional Information

Anna Karczewska
Affiliation: Department of Mathematics, University of Zielona Góra, ul. Szafrana 4a, 65-246 Zielona Góra, Poland
Email: A.Karczewska@im.uz.zgora.pl

Carlos Lizama
Affiliation: Departamento de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
Email: clizama@lauca.usach.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08487-5
PII: S 0002-9939(06)08487-5
Keywords: Stochastic Volterra equation, function-valued solutions, equations on a torus, spatially homogeneous Wiener process
Received by editor(s): April 15, 2005
Received by editor(s) in revised form: August 25, 2005
Published electronically: August 2, 2006
Additional Notes: The second author was supported in part by FONDECYT Grant #1050084
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.