Invariant Manifolds for Weak Solutions to Stochastic Equations

Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C2 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 C2 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.


Published in:
Probability Theory and Related Fields, 118(3), 323-341
Year:
2000
Publisher:
Springer Verlag
ISSN:
0178-8051
Laboratories:




 Record created 2010-04-25, last modified 2018-03-17

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