Stochastic differential equations
- 24 October 1955
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 51 (4) , 663-677
- https://doi.org/10.1017/s0305004100030735
Abstract
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) asmean-squareconvergence. 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.Keywords
This publication has 16 references indexed in Scilit:
- Stochastic Problems in Physics and AstronomyReviews of Modern Physics, 1943
- On Integration in Vector SpacesTransactions of the American Mathematical Society, 1938
- Uniformity in Linear SpacesTransactions of the American Mathematical Society, 1938
- On integration in vector spacesTransactions of the American Mathematical Society, 1938
- Uniformity in linear spacesTransactions of the American Mathematical Society, 1938
- A note on regular Banach spacesBulletin of the American Mathematical Society, 1938
- OSTEOLOGY, MYOLOGY, AND PROBABLE EVOLUTION OF THE NEMATOGNATH PELVIC GIRDLEAnnals of the New York Academy of Sciences, 1937
- Riemann integration and Taylor’s theorem in general analysisTransactions of the American Mathematical Society, 1927
- Riemann Integration and Taylor's Theorem in General AnalysisTransactions of the American Mathematical Society, 1927
- Sur Les Fonctionnelles BilineairesTransactions of the American Mathematical Society, 1915