On stopping Fock-space processes

2013/11/19 by Belton, Alexander C. R.
#46L53 #60G40 (secondary) #81S25 (primary) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1311.4871

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.

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