The Annals of Mathematical Statistics

Transforms of Stochastic Processes

P. Warwick Millar

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 39, Number 2 (1968), 372-376.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698398

Digital Object Identifier
doi:10.1214/aoms/1177698398

Mathematical Reviews number (MathSciNet)
MR225372

Zentralblatt MATH identifier
0155.23604

JSTOR
links.jstor.org

Citation

Millar, P. Warwick. Transforms of Stochastic Processes. Ann. Math. Statist. 39 (1968), no. 2, 372--376. doi:10.1214/aoms/1177698398. https://projecteuclid.org/euclid.aoms/1177698398


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