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Proceedings of the London Mathematical Society Advance Access published online on July 16, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp028
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© 2009 London Mathematical Society

Peano's theorem for rough differential equations in infinite-dimensional Banach spaces

Michael Caruana

Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom

Received 12 November 2008. Revision received 7 May 2009.

We present a proof for Peano's theorem for rough differential equations, which is valid in infinite dimensions under an appropriate compactness assumption on the vector fields. Our approach makes full use of Lyons’ Universal Limit Theorem and is based on the construction of a family of rough polynomial approximations, each of which is a concatenation of rough path solutions of different equations.

2000 Mathematics Subject Classification 60H10, 34A99.

The author was supported by EPSRC grant EP/E048609/1.


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