Series of iterated quantum stochastic integrals. (English) Zbl 1138.81461

Attal, Stéphane; Hudson, Robin L.

Azéma, J. (ed.) et al., Séminaire de Probabilités XXXIV. Berlin: Springer (ISBN 3-540-67314-8). Lect. Notes Math. 1729, 157-170 (2000).

Summary: We consider series of iterated non-commutative stochastic integrals of scalar operators on the boson Fock space. We give a sufficient condition for these series to converge and to define a reasonable operator. An application of this criterion gives a condition for the convergence of some formal series of generalized integrator processes such as considered in [P. B. Cohen et al., Int. J. Theor. Phys. 34, No. 8, 1481–1486 (1995; Zbl 0850.81035)].
For the entire collection see [Zbl 0940.00007].

MSC:

81S25	Quantum stochastic calculus
46L60	Applications of selfadjoint operator algebras to physics
47N50	Applications of operator theory in the physical sciences
60H05	Stochastic integrals

Citations:

Zbl 0850.81035