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