Quantum stochastic calculus on Boolean Fock space

被引：12

作者：

Ben Ghorbal, A ^{[1
]}

Schürmann, M ^{[1
]}

机构：

[1] Ernst Moritz Arndt Univ Greifswald, Inst Math & Informat, D-17487 Greifswald, Germany

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2004年 / 7卷 / 04期

关键词：

quantum stochastic calculus; Boolean independence; dilation; quantum dynamical semigroup;

D O I：

10.1142/S0219025704001815

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish a theory of stochastic integration with respect to the basic field operator processes in the Boolean case. This leads to a Boolean version of quantum Ito's product formula and has applications to the theory of dilations of quantum dynamical semigroups.

引用

页码：631 / 650

页数：20

共 20 条

[1] A REPRESENTATION FREE QUANTUM STOCHASTIC CALCULUS [J].

ACCARDI, L ;

FAGNOLA, F ;

QUAEGEBEUR, J .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 104 (01) :149-197

[2]

[Anonymous], 1973, PROBABILITY INFORM T

[3] FERMION ITO FORMULA AND STOCHASTIC EVOLUTIONS [J].

APPLEBAUM, DB ;

HUDSON, RL .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 96 (04) :473-496

[4] Non-commutative notions of stochastic independence [J].

Ben Ghorbal, A ;

Schürmann, M .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2002, 133 :531-561

[5] Tensor product systems of Hilbert modules and dilations of completely positive semigroups [J].

Bhat, BVR ;

Skeide, M .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2000, 3 (04) :519-575

[6]

BOZEJKO M, 1987, J REINE ANGEW MATH, V377, P170

[7]

DOGAN H, 2000, THESIS U HEIDELBERG

[8] TIME-ORTHOGONAL UNITARY DILATIONS AND NONCOMMUTATIVE FEYNMAN-KAC FORMULAS [J].

HUDSON, RL ;

ION, PDF ;

PARTHASARATHY, KR .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 83 (02) :261-280

[9] QUANTUM ITOS FORMULA AND STOCHASTIC EVOLUTIONS [J].

HUDSON, RL ;

PARTHASARATHY, KR .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 93 (03) :301-323

[10] STOCHASTIC INTEGRATION ON THE CUNTZ ALGEBRA 0-INFINITY [J].

KUMMERER, B ;

SPEICHER, R .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 103 (02) :372-408

← 1 2 →