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Journal of Theoretical Probability

, Volume 32, Issue 1, pp 484–526 | Cite as

On Stopping Fock-Space Processes

  • Alexander C. R. BeltonEmail author
Article
  • 49 Downloads

Abstract

We consider the theory of stopping bounded processes within the framework of Hudson–Parthasarathy quantum stochastic calculus, for both identity and vacuum adaptedness. This provides significant new insight into Coquio’s method of stopping (J Funct Anal 238:149–180, 2006). Vacuum adaptedness is required to express certain quantum stochastic representations, and many results, including the proof of the optional-sampling theorem, take a more natural form.

Keywords

Quantum stopping time Quantum stop time Quantum stochastic calculus Regular quantum semimartingale Regular \(\varOmega \)-semimartingale 

Mathematics Subject Classification (2010)

Primary: 81S25 Secondary: 46L53 60G40 

Notes

Acknowledgements

The author is grateful for the referee’s comments on a previous version of this work.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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