Author:
Ettaieb Aymen,Turki Khalifa Narjess,Ouerdiane Habib
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.
Subject
Statistics and Probability,Analysis