Operator-Valued Stochastic Differential Equations Arising from Unitary Group Representations

David Applebaum ()
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David Applebaum: Nottingham Trent University

Journal of Theoretical Probability, 2001, vol. 14, issue 1, 61-76

Abstract: Abstract Let π be a unitary representation of a Lie group G and (φ(t), t≥0) be a Lévy process in G. Using analytic vector techniques it is shown that the unitary process U(t)=π(φ(t)) satisfies an operator-valued stochastic differential equation. The prescription J(t) π(f)=U(t) π(f) U(t)* gives rise to an algebraic stochastic flow on the algebra generated by operators of the form π(f)=∫ f(g) π(g) dg where f is in the group algebra and dg is a left Haar measure. J(t) itself satisfies an operator-valued stochastic differential equation of a type which has been previously studied within the context of quantum stochastic calculus.

Keywords: stochastic differential equations; unitary group representations (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1007816930696

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