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April, 1968 Transforms of Stochastic Processes
P. Warwick Millar
Ann. Math. Statist. 39(2): 372-376 (April, 1968). DOI: 10.1214/aoms/1177698398


In this note, the notion of an optimal transform of a (discrete parameter) stochastic process is introduced. Such transforms are shown to exist in certain cases, and a relationship to optimal stopping times is discussed. These ideas lead naturally to the representation of any given stochastic process as the transform of a submartingale. This type of representation theorem is extended to continuous parameter processes, where it is shown that in certain cases a quasi-martingale can be represented as a stochastic integral with respect to a submartingale.


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P. Warwick Millar. "Transforms of Stochastic Processes." Ann. Math. Statist. 39 (2) 372 - 376, April, 1968.


Published: April, 1968
First available in Project Euclid: 27 April 2007

zbMATH: 0155.23604
MathSciNet: MR225372
Digital Object Identifier: 10.1214/aoms/1177698398

Rights: Copyright © 1968 Institute of Mathematical Statistics

Vol.39 • No. 2 • April, 1968
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