Open Access
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


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.


Download Citation

M. Emery. "A Generalization of Stochastic Integration with Respect to Semimartingales." Ann. Probab. 10 (3) 709 - 727, August, 1982.


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

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

Primary: 60G48
Secondary: 60G07 , 60H05

Keywords: general theory of processes , Semimartingales , stochastic integration

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
Back to Top