Quantum Feynman-Kac perturbations

Belton, Alexander C. R. and Lindsay, J. Martin and Skalski, Adam G. (2014) Quantum Feynman-Kac perturbations. Journal of the London Mathematical Society, 89 (1). pp. 275-300. ISSN 0024-6107

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We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterised under alternative assumptions of separability or Markov regularity. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.

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Journal Article
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Journal of the London Mathematical Society
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24 Jan 2013 05:34
Last Modified:
21 Nov 2022 22:46