Realization of Unitary q-White Noise on Fock Space

Michael Schürmann
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Michael Schürmann: Universität Heidelberg, Institut für Angewandte Mathematik

A chapter in Probability Measures on Groups X, 1991, pp 377-386 from Springer

Abstract: Abstract We consider families (U t ) t ≥0 of unitary operators on C d ⊗ H, d ∊ ℕ, ℍ a Hilbert space, which have the property that the multiplicative increments for disjoint intervals satisfy certain q-commutation relations with q a complex number of modulus 1. Under additional assumptions on (U t ) t ≥0 which are motivated by classical stochastic processes with independent, stationary increments taking values in the group of unitary d × d-matrices, we give a realization of (U t ) t ≥0 as the solution of a linear quantum stochastic differential equation on Boson Fock space.

Keywords: Algebra Homomorphism; Stationary Increment; Grade Vector Space; Positive Linear Functional; Quantum Stochastic Differential Equation (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2364-6_28

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DOI: 10.1007/978-1-4899-2364-6_28

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