Malliavin calculus for quantum stochastic processes

被引：3

作者：

Franz, U

Léandre, R

Schott, R

机构：

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

[2] Univ Nancy 1, Inst Elie Cartan, F-54506 Vandoeuvre Nancy, France

[3] Univ Nancy 1, LORIA, F-54506 Vandoeuvre Nancy, France

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1999年 / 328卷 / 11期

关键词：

D O I：

10.1016/S0764-4442(99)80325-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A Girsanov formula and an integration by parts formula are given for quantum stochastic processes on the Heisenberg-Weyl algebra and used to obtain sufficient conditions for their Wigner density in a given state to lie in the Sobolev space of order k. (C) Academie des Sciences/Elsevier, Paris.

引用

页码：1061 / 1066

页数：6

共 10 条

[1]

[Anonymous], P INT S STOCH DIFF E

[2]

Folland G. B., 1989, HARMONIC ANAL PHASE

[3]

MALLIAVIN P, 1997, FUND PRINC MATH SCI, V313

[4]

MEYER PA, 1986, LECT NOTES MATH, V1204, P244

[5]

MEYER PA, 1993, QUANTUM CALCULUS REL

[6]

NUALART D, 1995, PROBAB ITS APPL

[7]

Parthasarathy K., 1992, Monographs in Mathematics

[8] THE MALLIAVIN CALCULUS, A FUNCTIONAL ANALYTIC APPROACH [J].

STROOCK, DW .

JOURNAL OF FUNCTIONAL ANALYSIS, 1981, 44 (02) :212-257

[9]

Weyl H, 1931, THEORY GROUPS QUANTU

[10] On the quantum correction for thermodynamic equilibrium [J].

Wigner, E .

PHYSICAL REVIEW, 1932, 40 (05) :0749-0759

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