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A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

Published online by Cambridge University Press:  05 October 2009

A. JENTZEN
Affiliation:
Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany (email: jentzen@math.uni-frankfurt.de)
P. E. KLOEDEN*
Affiliation:
Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany (email: kloeden@math.uni-frankfurt.de)
*
For correspondence; e-mail: kloeden@math.uni-frankfurt.de
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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.

Type
Research Article
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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