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Kholevo, A. S.

Quantum stochastic calculus. (English. Russian original) Zbl 0732.60066

J. Sov. Math. 56, No. 5, 2609-2624 (1991); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Noveishie Dostizh. 36, 3-28 (1989).
The main aim of this paper is to introduce the reader into the quantum stochastic calculus in the symmetric Fock space from the stochastic processes point of view. The author discusses the quantum Itô formula, applications to probabilistic representations of solutions of differential equations, and applications to extensions of dynamical semigroups. New algebraic relations are given for chronologically ordered exponents which are similar to stochastic semigroups in the classical probability theory.
Reviewer: Sh.A.Ayupov (Tashkent)

Cited in 11 Documents

MSC:

81S25 Quantum stochastic calculus
60H05 Stochastic integrals
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46L55 Noncommutative dynamical systems
60G99 Stochastic processes

Keywords:

quantum stochastic calculus; symmetric Fock space; quantum Itô formula; chronologically ordered exponents
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References:

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