Existence of invariant manifolds for stochastic equations in infinite dimension |
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Authors: | Damir Filipovi? Josef Teichmann |
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Affiliation: | a Department of Operations Research and Financial Engineering, Princeton, University Princeton, NJ, 08544, USA b Institute of Financial and Actuarial Mathematics, TU Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria |
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Abstract: | We provide a Frobenius type existence result for finite-dimensional invariant submanifolds for stochastic equations in infinite dimension, in the spirit of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, UK, 1992). We recapture and make use of the convenient calculus on Fréchet spaces, as developed by Kriegl and Michor (The Convenient Setting for Global Analysis, Surveys and Monographs, Vol. 53, Amer. Math. Soc., Providence, RI, 1997). Our main result is a weak version of the Frobenius theorem on Fréchet spaces. As an application, we characterize all finite-dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates. |
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Keywords: | Affine term structure Analysis on Frechet spaces Finite-dimensional invariant submanifolds Frobenius theorem Interest rate models |
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