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July 2019 Remarks on Föllmer's pathwise Itô calculus
Yuki Hirai
Osaka J. Math. 56(3): 631-660 (July 2019).

Abstract

We extend some results about Föllmer's pathwise Itô calculus that have only been derived for continuous paths to càdlàg paths with quadratic variation. We study some fundamental properties of pathwise Itô integrals with respect to càdlàg integrators, especially associativity and the integration by parts formula. Moreover, we study integral equations with respect to pathwise Itô integrals. We prove that some classes of integral equations, which can be explicitly solved in the usual stochastic calculus, can also be solved within the framework of Föllmer's calculus.

Citation

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Yuki Hirai. "Remarks on Föllmer's pathwise Itô calculus." Osaka J. Math. 56 (3) 631 - 660, July 2019.

Information

Published: July 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07108033
MathSciNet: MR3981304

Subjects:
Primary: 60H99
Secondary: 60H05

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 3 • July 2019
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