On Stopping Fock-Space Processes

On Stopping Fock-Space Processes

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 req...

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Veröffentlicht in:Journal of theoretical probability 2019-03, Vol.32 (1), p.484-526
1. Verfasser: Belton, Alexander C. R.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Zusammenfassung: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-018-0851-z