Noncommutative Itô and Stratonovich noise and stochastic evolutions

J. Gough*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)

Abstract

We complete the theory of noncommutative stochastic calculus by introducing the Stratonovich representation. The key idea is to develop a theory of white noise analysis for both the Itô and Stratonovich representations based on distributions over piecewise continuous functions mapping into a Hilbert space. As an example, we derive the most general class of unitary stochastic evolutions, where the Hilbert space is the space of complex numbers, by first constructing the evolution in the Stratonovich representation where unitarity is self-evident.

Original languageEnglish
Pages (from-to)1431-1437
Number of pages7
JournalTheoretical and Mathematical Physics
Volume113
Issue number2
DOIs
Publication statusPublished - Nov 1997
Externally publishedYes

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