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Regularity of solutions to stochastic Volterra equations with infinite delay
Author(s):
Anna
Karczewska;
Carlos
Lizama
Journal:
Proc. Amer. Math. Soc.
135
(2007),
531-540.
MSC (2000):
Primary 60H20;
Secondary 60H05, 45D05.
Posted:
August 2, 2006
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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  -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:
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
Posted:
August 2, 2006
Additional Notes:
The second author was supported in part by FONDECYT Grant \#1050084
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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