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.
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Received: 15 April 1999 / Revised version: 4 February 2000 / Published online: 18 September 2000
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Filipović, D. Invariant manifolds for weak solutions to stochastic equations. Probab Theory Relat Fields 118, 323–341 (2000). https://doi.org/10.1007/PL00008744
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DOI: https://doi.org/10.1007/PL00008744
Keywords
- Manifold
- Hilbert Space
- Weak Solution
- Rate Curve
- Strong Solution