Regularity of finite-dimensional realizations for Evolution Equations

Details Regularity of finite-dimensional realizations for Evolution Equations Regularity of finite-dimensional realizations for Evolution Equations

2001-12-21

arxiv.org/abs/math/0112244v2

Journal of Functional Analysis 197 (2003), 433--446

Mathematics

Functional Analysis

Scientific paper

We show that a continuous local semiflow of $C^k$-maps on a finite-dimensional $C^k$-manifold M can be embedded into a local $C^k$-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are highly regular objects, namely given by submanifolds M of $D(A^{\infty})$, where A is the generator of a strongly continuous semigroup.

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