Quantum white noise Feynman–Kac formula

Quantum white noise Feynman–Kac formula AbstractIn this paper, we give a probabilistic representation of the heat equation associated with the quantum K-Gross Laplacian usinginfinite-dimensional stochastic calculus in two variables. Applying the heat semigroup to the particular case where the operator is the multiplication one, we establish a relation between the classical and the quantum heat semigroup. Finally, using acombination between convolution calculus and the generalized stochastic calculus, we give a generalization of the Feynman–Kacformula. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Random Operators and Stochastic Equations de Gruyter

Quantum white noise Feynman–Kac formula

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Publisher
De Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1569-397X
eISSN
1569-397X
D.O.I.
10.1515/rose-2018-0007
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper, we give a probabilistic representation of the heat equation associated with the quantum K-Gross Laplacian usinginfinite-dimensional stochastic calculus in two variables. Applying the heat semigroup to the particular case where the operator is the multiplication one, we establish a relation between the classical and the quantum heat semigroup. Finally, using acombination between convolution calculus and the generalized stochastic calculus, we give a generalization of the Feynman–Kacformula.

Journal

Random Operators and Stochastic Equationsde Gruyter

Published: Jun 1, 2018

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