The Annals of Probability

Generalized Integration and Stochastic ODEs

Franco Flandoli and Francesco Russo

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Stochastic forward integrals for processes more general than semimartingales are shown to exist, generalized forms of Itô–Wentzell formula and covariation formula are proved, and one-dimensional stochastic equations driven by finite quadratic variation processes and semimartingales are solved. This generalized stochastic calculus is motivated by applications to uniqueness and dependence on parameters for stochastic equations with nonregular drift.

Article information

Ann. Probab., Volume 30, Number 1 (2002), 270-292.

First available in Project Euclid: 29 April 2002

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Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60H10: Stochastic ordinary differential equations [See also 34F05]

Forward stochastic integration generalized Itô-Wentsell formula finite quadratic variations process


Flandoli, Franco; Russo, Francesco. Generalized Integration and Stochastic ODEs. Ann. Probab. 30 (2002), no. 1, 270--292. doi:10.1214/aop/1020107768.

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