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Random Operators and Stochastic Equations

Quantum white noise Feynman–Kac formula

Aymen Ettaieb, Narjes Turki Khalifa, Habib Ouerdiane

Published May 15, 2018• 2 citations
Publisher

Abstract

Abstract In this paper, we give a probabilistic representation of the heat equation associated with the quantum K-Gross Laplacian using infinite-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 a combination between convolution calculus and the generalized stochastic calculus, we give a generalization of the Feynman–Kac formula.

DOI
10.1515/rose-2018-0007

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