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2022 Simplified stochastic calculus via semimartingale representations
Aleš Černý, Johannes Ruf
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Electron. J. Probab. 27: 1-32 (2022). DOI: 10.1214/21-EJP729

Abstract

We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment of real-valued and complex-valued semimartingales. The proposed calculus is a blueprint for the derivation of new relationships among stochastic processes with specific examples provided below.

Acknowledgments

We thank Jan Kallsen, Christoph Kühn, Johannes Muhle-Karbe, Pietro Siorpaes, two anonymous referees, and an associate editor for helpful comments and suggestions.

Citation

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Aleš Černý. Johannes Ruf. "Simplified stochastic calculus via semimartingale representations." Electron. J. Probab. 27 1 - 32, 2022. https://doi.org/10.1214/21-EJP729

Information

Received: 9 October 2020; Accepted: 7 December 2021; Published: 2022
First available in Project Euclid: 12 January 2022

arXiv: 2006.11914
Digital Object Identifier: 10.1214/21-EJP729

Subjects:
Primary: 60G07 , 60G44 , 60G48 , 60H05 , 60H05

Keywords: complex-valued process , Émery formula , generalized Yor formula , Itô formula , semimartingale representation

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