Quantum Stochastic Calculus Associated With Quantum Lévy White Noise
Corresponding Author
Omar Alzeley
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Makkah, Saudi Arabia
Correspondence:
Omar Alzeley ([email protected])
Contribution: Investigation, Methodology, Writing - review & editing
Search for more papers by this authorAymen Ettaieb
Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, Tunis, Tunisia
Contribution: Investigation, Writing - review & editing, Methodology
Search for more papers by this authorHafedh Rguigui
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Makkah, Saudi Arabia
High School of Sciences and Technology of Hammam Sousse, University of Sousse, Hammam Sousse, Tunisia
Contribution: Conceptualization, Investigation, Writing - original draft, Supervision, Writing - review & editing, Project administration
Search for more papers by this authorCorresponding Author
Omar Alzeley
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Makkah, Saudi Arabia
Correspondence:
Omar Alzeley ([email protected])
Contribution: Investigation, Methodology, Writing - review & editing
Search for more papers by this authorAymen Ettaieb
Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, Tunis, Tunisia
Contribution: Investigation, Writing - review & editing, Methodology
Search for more papers by this authorHafedh Rguigui
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Makkah, Saudi Arabia
High School of Sciences and Technology of Hammam Sousse, University of Sousse, Hammam Sousse, Tunisia
Contribution: Conceptualization, Investigation, Writing - original draft, Supervision, Writing - review & editing, Project administration
Search for more papers by this authorFunding: This research work was funded by Umm Al-Qura University, Saudi Arabia under grant number: 25UQU4340203GSSR01.
ABSTRACT
We establish the commutation relations of the quantum Lévy operators, consisting of the generalized Lévy Gross Laplacian and its adjoint, annihilation operator, creation operator, and the Lévy number operator. In particular, such quantum Lévy operators span a nonsolvable -Lie algebra. We then give a generalization of the Hudson–Parthasarathy stochastic integrals in terms of the quantum Lévy operators and derive a noncommutative Itô formula.
Conflicts of Interest
The authors declare no conflicts of interest.
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