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Wiener processes on manifolds of maps

Published online by Cambridge University Press:  14 November 2011

Peter Baxendale
Peter Baxendale
Affiliation:
Department of Mathematics, King's College, Aberdeen, Scotland
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Synopsis

The solutions of stochastic differential equations are used to construct Markov processes on the Banach manifold C(S, M) of continuous maps from a compact metric space S into a smooth complete finite dimensional Riemannian manifold M. In the special case where S is a single point the construction gives a large class of diffusion processes on the manifold M, including (under certain curvature conditions) the Brownian motion process.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 1-2 , 1980 , pp. 127 - 152
Copyright
Copyright © Royal Society of Edinburgh 1980

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