The Annals of Probability

Generalized Integration and Stochastic ODEs

Franco Flandoli and Francesco Russo

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Abstract

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

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

Dates
First available in Project Euclid: 29 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1020107768

Digital Object Identifier
doi:10.1214/aop/1020107768

Mathematical Reviews number (MathSciNet)
MR1894108

Zentralblatt MATH identifier
1022.60054

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

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

Citation

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


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