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Title: Quantum stopping times stochastic integral in the interacting Fock space

Following the ideas of Hudson [J. Funct. Anal. 34(2), 266-281 (1979)] and Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)], we define a quantum stopping time (QST, for short) τ in the interacting Fock space (IFS, for short), Γ, over L{sup 2}(ℝ{sup +}), which is actually a spectral measure in [0, ∞] such that τ([0, t]) is an adapted process. Motivated by Parthasarathy and Sinha [Probab. Theory Relat. Fields 73, 317-349 (1987)] and Applebaum [J. Funct. Anal. 65, 273-291 (1986)], we also develop a corresponding quantum stopping time stochastic integral (QSTSI, for abbreviations) on the IFS over a subspace of L{sup 2}(ℝ{sup +}) equipped with a filtration. As an application, such integral provides a useful tool for proving that Γ admits a strong factorisation, i.e., Γ = Γ{sub τ]} ⊗ Γ{sub [τ}, where Γ{sub τ]} and Γ{sub [τ} stand for the part “before τ” and the part “after τ,” respectively. Additionally, this integral also gives rise to a natural composition operation among QST to make the space of all QSTs a semigroup.
Authors:
 [1]
  1. College of Mathematics Science, Chong Qing Normal University, Chongqing 400047 (China)
Publication Date:
OSTI Identifier:
22479587
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FILTRATION; INTEGRALS; SPACE; STOCHASTIC PROCESSES