Invariant Manifolds For Weak Solutions To Stochastic Equations 2000


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Invariant
J-invariant
Hopf invariant
  • Hopf invariant

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Lagrange invariant
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Kontsevich invariant

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  • Author:  by Damir Filipovic

  • 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. 1. Introduction Consider a stochastic equation dX t = (AX t + F (t, X t )) dt +B(t,X t ) dW t X 0 = x 0 (1) on a separable Hilbert space H . Here W denotes a Q-Wiener process on some separable Hilbert space G. The operator A is the infinitesimal generator of a strongly continuous semigroup in H . The random mappings F = F (t, #, x) and B = B(t, #, x) satisfy appropriate measurability conditions. This paper studies the stochastic v...

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