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Simplified stochastic calculus via semimartingale representations (2006.11914v5)
Published 21 Jun 2020 in math.PR and q-fin.MF
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.
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