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April, 1979 A Comparison of Stochastic Integrals
Philip Protter
Ann. Probab. 7(2): 276-289 (April, 1979). DOI: 10.1214/aop/1176995088


Two different stochastic integrals have been developed during the last ten years. One is largely associated with the work of E. J. McShane (the star integral), and the other has grown out of the work of H. Kunita and S. Watanabe (the dot integral). Assuming the customary conditions that guarantee the existence of the star integral, we give a formula relating the two integrals. We show that the star integral is equal to the dot integral provided one takes a projection of the integrand onto the space of predictable processes before evaluating the dot integral. This essentially embeds the theory of the star integral into that of the dot integral.


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Philip Protter. "A Comparison of Stochastic Integrals." Ann. Probab. 7 (2) 276 - 289, April, 1979.


Published: April, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0404.60062
MathSciNet: MR525054
Digital Object Identifier: 10.1214/aop/1176995088

Primary: 60H05
Secondary: 60H10 , 60H20

Keywords: Semimartingales , stochastic integrals

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 2 • April, 1979
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