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Regularity of finite-dimensional realizations for evolution equations. (English) Zbl 1011.37004
Summary: We show that a continuous local semiflow of \(C^k\)-maps on a finite-dimensional \(C^k\)-manifold \(M\) with boundary is in fact a local \(C^k\)-semiflow on \(M\) and can be embedded into a local \(C^k\)-flow around interior points of \(M\) under some weak assumption. This result is applied to an open regularity problem for finite-dimensional realizations of stochastic interest rate models.

MSC:
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37H10 Generation, random and stochastic difference and differential equations
35B65 Smoothness and regularity of solutions to PDEs
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
91B28 Finance etc. (MSC2000)
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