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Stochastic differential equations

Published online by Cambridge University Press:  24 October 2008

D. A. Edwards  and
J. E. Moyal
D. A. Edwards
Affiliation:
Oriel College Oxford
J. E. Moyal
Affiliation:
Department of Mathematics University Of Manchester
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Extract

The work of which this paper is an account began as a study of differential equations for functions whose values are random variables of finite variance. It was intended that all questions of convergence should be treated from the standpoint of strong convergence in Hilbert space—familiar to probabilists from the writings of Karhunen(11) and Loève(13) as mean-square convergence. The more general Banach-space approach now adopted was made possible by the discovery of a theorem (Theorem 1 of this paper) which Mr D. G. Kendall, its apparent author, kindly communicated to us.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 4 , October 1955 , pp. 663 - 677
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

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