Quantum martingales and stochastic integrals. (English) Zbl 0642.46053
Quantum probability and applications III, Proc. Conf., Oberwolfach/FRG 1987, Lect. Notes Math. 1303, 363-373 (1988).
[For the entire collection see Zbl 0627.00022.]
This paper is concerned with non-commutative stochastic integration. There are some results, for instance, the stochastic calculus of Brownian motion in non-commutative theories, say the martingale representation theorem, the fermion Itô-Clifford theory and the quasi-free fermion theory.
The author gives elementary proofs of these theorems, furthermore, he shows that in the quasi-free case boundedness of the one-particle operator is not necessary.
This paper is concerned with non-commutative stochastic integration. There are some results, for instance, the stochastic calculus of Brownian motion in non-commutative theories, say the martingale representation theorem, the fermion Itô-Clifford theory and the quasi-free fermion theory.
The author gives elementary proofs of these theorems, furthermore, he shows that in the quasi-free case boundedness of the one-particle operator is not necessary.
Reviewer: A.Wehrl
MSC:
| 46L51 | Noncommutative measure and integration |
| 46L53 | Noncommutative probability and statistics |
| 46L54 | Free probability and free operator algebras |
| 60G48 | Generalizations of martingales |
| 60H05 | Stochastic integrals |
