Well-posedness of QSDEs driven by fermion Brownian motion in
noncommutative Lp -space
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.
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