Invariant manifolds for weak solutions to stochastic equations |
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Authors: | Damir Filipovi? |
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Institution: | Department of Mathematics, ETH, R?mistrasse 101, CH-8092 Zürich, Switzerland. e-mail: filipo@math.ethz.ch, CH
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Abstract: | Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C
2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: any weak solution, which is viable in
a finite dimensional C
2 submanifold, is a strong solution.
These results are related to finding finite dimensional realizations for stochastic equations. There has recently been increased
interest in connection with a model for the stochastic evolution of forward rate curves.
Received: 15 April 1999 / Revised version: 4 February 2000 / Published online: 18 September 2000 |
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Keywords: | |
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