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.| File | Dimensione | Formato | |
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