Assuming that a probability measure on ℝd has finite moments of any order, its moments are completely determined by two family of operators. The first family is composed of the neutral (preservation) operators. The second family consists of the commutators between the annihilation and creation operators. As a confirmation of this fact, a characterization of the Gaussian probability measures in terms of these two families of operators is given. The proof of this characterization relies on a simple combinatorial identity.

Accardi, L., Kuo, H., Stan, A. (2007). A combinatorial identity and its application to Gaussian measures. In Quantum probability and infinite dimensional analysis: proceedings of the 26th Conference, Levico, Italy, 20–26 February 2005 / edited by L. Accardi, W. Freudenberg, M. Schürmann (pp.1-12). World Scientific Publishing Society [10.1142/9789812770271_0001].

A combinatorial identity and its application to Gaussian measures

ACCARDI, LUIGI;
2007-07-01

Abstract

Assuming that a probability measure on ℝd has finite moments of any order, its moments are completely determined by two family of operators. The first family is composed of the neutral (preservation) operators. The second family consists of the commutators between the annihilation and creation operators. As a confirmation of this fact, a characterization of the Gaussian probability measures in terms of these two families of operators is given. The proof of this characterization relies on a simple combinatorial identity.
Quantum probability and infinite dimensional analysis
Levico (Italy)
2005
26.
Rilevanza internazionale
contributo
feb-2005
Settore MAT/06 - Probabilita' e Statistica Matematica
English
commutator; annihilation operator; creation operator; neutral (preservation) operator
Intervento a convegno
Accardi, L., Kuo, H., Stan, A. (2007). A combinatorial identity and its application to Gaussian measures. In Quantum probability and infinite dimensional analysis: proceedings of the 26th Conference, Levico, Italy, 20–26 February 2005 / edited by L. Accardi, W. Freudenberg, M. Schürmann (pp.1-12). World Scientific Publishing Society [10.1142/9789812770271_0001].
Accardi, L; Kuo, H; Stan, A
File in questo prodotto:
File Dimensione Formato  
A Combinatory Identity and its Application to Gaussian Measures.pdf

accesso aperto

Dimensione 521.24 kB
Formato Adobe PDF
521.24 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/44030
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact