Simplified stochastic calculus via semimartingale representations
arXiv:2006.11914 · 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.
32 pages; updated references; fixed a small typo in proof of T3.17