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Invariant manifolds for weak solutions to stochastic equations
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  • Published: November 2000

Invariant manifolds for weak solutions to stochastic equations

  • Damir Filipović1 

Probability Theory and Related Fields volume 118, pages 323–341 (2000)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, ETH, Rämistrasse 101, CH-8092 Zürich, Switzerland. e-mail: filipo@math.ethz.ch, , , , , , CH

    Damir Filipović

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  1. Damir Filipović
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Additional information

Received: 15 April 1999 / Revised version: 4 February 2000 / Published online: 18 September 2000

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Cite this article

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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  • Issue Date: November 2000

  • DOI: https://doi.org/10.1007/PL00008744

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Keywords

  • Manifold
  • Hilbert Space
  • Weak Solution
  • Rate Curve
  • Strong Solution
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