Habib Ouerdiane, Samah Horrigue
Published 2008-04-24Version 1
In this paper, we introduce and study a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian. Then, applying the quantum Gross Laplacian to the particular case where the operator is the multiplication operator, we find a relation between classical and quantum Gross Laplacian. As application, we give explicit solution of linear quantum white noise differential equation. In particular, we give a explicit solution of the quantum Gross heat equation.
Maximum principle for SPDEs and its applications
Strong Solution of Backward Stochastic Partial Differential Equations in $C^2$ Domains
Harnack Inequalities and Applications for Ornstein-Uhlenbeck Semigroups with Jump
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