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Well-posedness of QSDEs driven by fermion Brownian motion in noncommutative Lp -space
  • Shan Wang,
  • Guangdong Jing,
  • Penghui Wang
Shan Wang
Shandong University School of Mathematics

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Guangdong Jing
Shandong University School of Mathematics
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Penghui Wang
Shandong University School of Mathematics
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Abstract

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space L p ( C ) for p>2. We investigate the existence and uniqueness of L p -solution of quantum stochastic differential equations in infinite time horizon by the Burkholder-Gundy inequalities for noncommutative martingales given by Pisier and Xu. Finally, we obtain Markov property and the self-adjointness which is of great significance in the study of optimal control problems. 2020 AMS Subject Classification: 46L51, 47J25, 60H10, 81J25.
28 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
28 Aug 2023Submission Checks Completed
28 Aug 2023Assigned to Editor
05 Sep 2023Review(s) Completed, Editorial Evaluation Pending
05 Sep 2023Reviewer(s) Assigned
10 Oct 2023Editorial Decision: Revise Major
13 Nov 20231st Revision Received
16 Nov 2023Submission Checks Completed
16 Nov 2023Assigned to Editor
16 Nov 2023Review(s) Completed, Editorial Evaluation Pending
16 Nov 2023Reviewer(s) Assigned