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A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

Part of: Stochastic analysis

Published online by Cambridge University Press:  05 October 2009

A. JENTZEN  and
P. E. KLOEDEN
A. JENTZEN
Affiliation:
Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany (email: [email protected])
P. E. KLOEDEN*
Affiliation:
Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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An existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise.

Keywords

stochastic partial differential equationexistence and uniqueness theoremspace–time white noisetrace-class noise

MSC classification

Secondary: 60H15: Stochastic partial differential equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 33 - 46
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

This work has been supported by the DFG project ‘Pathwise numerics and dynamics of stochastic evolution equations’.

References

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