Barnett, Chris; Lyons, Terry Stopping non-commutative processes. (English) Zbl 0585.60058 Math. Proc. Camb. Philos. Soc. 99, 151-161 (1986). The paper discusses stopping times and stopping in the context of the Clifford probability gauge space. The authors show that \(L^ 2\)- martingales can be stopped and they demonstrate that the formalism is very similar to the commutative case. However they remain silent upon the question of whether or not one can stop processes other than \(L^ 2\)- martingales. Apart from the optional stopping theorem there is also a random time martingale convergence theorem. It would be interesting to know whether an ’almost everywhere’ version of this result holds. The example of a ”time” given in the final section of the paper should not be taken too seriously, the formalism developed in this paper shows only that adapted spectral families are time-like not that all adapted families are times. Cited in 2 ReviewsCited in 9 Documents MSC: 60H05 Stochastic integrals 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 60G44 Martingales with continuous parameter Keywords:non commutative probability; stopping times; Clifford probability gauge space; optional stopping theorem; random time martingale convergence theorem PDFBibTeX XMLCite \textit{C. Barnett} and \textit{T. Lyons}, Math. Proc. Camb. Philos. Soc. 99, 151--161 (1986; Zbl 0585.60058) Full Text: DOI References: [1] Barnett, J. Operator Theory 11 pp 255– (1984) [2] DOI: 10.1016/0022-1236(82)90066-0 · Zbl 0492.46051 · doi:10.1016/0022-1236(82)90066-0 [3] Barnett, Glasgow Math. J 24 pp 71– (1983) [4] McShane, Stochastic Calculus and Stochastic Models (1974) · Zbl 0292.60090 [5] DOI: 10.1016/0047-259X(71)90027-3 · Zbl 0254.60031 · doi:10.1016/0047-259X(71)90027-3 [6] Dunford, Linear Operators (1958) [7] Kussmaul, Stochastic Integration and Generalised Martingales (1977) [8] Dunford, Linear Operators (1958) [9] DOI: 10.1016/0022-1236(79)90034-X · Zbl 0424.46048 · doi:10.1016/0022-1236(79)90034-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.