Heisenberg-Weyl Lie algebra and natural exponential families

被引：1

作者：

Mohammed, Zarai ^{[1
]}

机构：

[1] Univ Sfax, Fac Sci, Dept Math, Sfax, Tunisia

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2007年 / 10卷 / 02期

关键词：

natural exponential family; variance function; 2-orthogonal polynomials; lowering and raising operators;

D O I：

10.1142/S0219025707002749

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present in this work a specific construction of raising and lowering operators for 2-orthogonal quasi-monomial polynomials associated with continuous and discrete natural exponential families. We use these operators in order to characterize the real class of cubic natural exponential families.

引用

收藏

页码：293 / 301

页数：9

相关论文

共 10 条

[1] Interacting Fock spaces and Gaussianization of probability measures [J].

Accardi, L ;

Bozejko, M .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 1998, 1 (04) :663-670

[2] Characterization of probability measures through the canonically associated interacting Fock spaces [J].

Accardi, L ;

Kuo, HH ;

Stan, A .

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2004, 7 (04) :485-505

[3] Coherent states and squeezed states in interacting Fock space [J].

Das, PK .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2002, 41 (06) :1099-1106

[4]

Dattoli G., 1996, THEORY APPL GEN BESS

[5] SOME CLASSES OF ORTHOGONAL POLYNOMIALS ASSOCIATED WITH MARTINGALES [J].

FEINSILVER, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 98 (02) :298-302

[6] Characterization of the cubic exponential families by orthogonality of polynomials [J].

Hassairi, A ;

Zarai, M .

ANNALS OF PROBABILITY, 2004, 32 (3B) :2463-2476

[7] NATURAL REAL EXPONENTIAL-FAMILIES WITH CUBIC VARIANCE FUNCTIONS [J].

LETAC, G ;

MORA, M .

ANNALS OF STATISTICS, 1990, 18 (01) :1-37

[8]

Meixner J., 1934, J. London Math. Soc., V9, P6

[9] NATURAL EXPONENTIAL-FAMILIES WITH QUADRATIC VARIANCE FUNCTIONS [J].

MORRIS, CN .

ANNALS OF STATISTICS, 1982, 10 (01) :65-80

[10] LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL-EQUATIONS [J].

SMIRNOV, Y ;

TURBINER, A .

MODERN PHYSICS LETTERS A, 1995, 10 (24) :1795-1802