Brownian bridge in quantum probability

Kalyan B. Sinha ()
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Kalyan B. Sinha: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 4, 551-560

Abstract: Abstract The Classical Brownian Bridge is constructed in Symmetric Fock space over an appropriate base Hilbert space. While the representation of the classical Ito-Wiener integral with respect to the increments of the Brownian bridge implements the unitary isomorphism between the Fock space and the (classical) L2 space of the Brownian bridge (as is the case with the standard Brownian motion (SBM)), the quantum Ito-integrals with respect to the associated creation and annihilation bridge processes give different left-and right-integrals. This essentially displays the feature that the Brownian Bridge is not a process of independent increments.

Keywords: Fock space for Brownian bridge; Ito integrals; right- and left integrals (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0245-4

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