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Itô’s Lemma with quantum calculus (\(q\)-calculus): some implications. (English) Zbl 1211.81083

Summary: \(q\)-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in Itô’s lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a Itô Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with \(q\)-derivatives.

MSC:

81S25 Quantum stochastic calculus
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