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August, 1982 A Generalization of Stochastic Integration with Respect to Semimartingales
M. Emery
Ann. Probab. 10(3): 709-727 (August, 1982). DOI: 10.1214/aop/1176993779

Abstract

On the real line, there exist $\sigma$-finite measures which are not Radon measures, but are nevertheless defined on all bounded intervals $\big(\text{e.g.} \frac{1}{x} \sin \frac{1}{x} dx, \text{or} \sum_n\frac{(-1)^n}{n} \delta_{1/n}\big).$ Similarly, in stochastic calculus, there exist processes that, though not semimartingales, can be obtained as stochastic integrals of predictable processes with respect to semimartingales. This paper deals with such processes.

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M. Emery. "A Generalization of Stochastic Integration with Respect to Semimartingales." Ann. Probab. 10 (3) 709 - 727, August, 1982. https://doi.org/10.1214/aop/1176993779

Information

Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0489.60059
MathSciNet: MR659540
Digital Object Identifier: 10.1214/aop/1176993779

Subjects:
Primary: 60G48
Secondary: 60G07 , 60H05

Keywords: general theory of processes , Semimartingales , stochastic integration

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August, 1982
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