We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Well‐posedness of quantum stochastic differential equations driven by fermion Brownian motion in noncommutative Lp‐space.
- Authors
Jing, Guangdong; Wang, Penghui; Wang, Shan
- Abstract
This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space Lp(풞) for 2≤p<∞$$ 2\le p<\infty $$. First, we investigate the existence and uniqueness of Lp$$ {L}&#x0005E;p $$‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of Lp$$ {L}&#x0005E;p $$‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions.
- Subjects
STOCHASTIC differential equations; STOCHASTIC control theory; FERMIONS; STOCHASTIC systems; BROWNIAN motion; TIME perspective
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 8, p6990
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9953