By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate Lévy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is known as time-space harmonic polynomials. Then, simple closed-form expressions of some multivariate classical families of polynomials are given. The main advantage of this symbolic representation is the plainness of the setting which reduces to few fundamental statements but also of its implementation in any symbolic software. The role played by cumulants is emphasized within the generalized Hermite polynomials. The new class of multivariate Lévy-Sheffer systems is introduced.
Multivariate time-space harmonic polynomials: a symbolic approach / Di Nardo, Elvira; Oliva, Immacolata. - In: MATHEMATICAL METHODS IN ECONOMICS AND FINANCE. - ISSN 1971-6419. - 7:1(2012), pp. 41-56.
Multivariate time-space harmonic polynomials: a symbolic approach
Immacolata Oliva
2012
Abstract
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate Lévy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is known as time-space harmonic polynomials. Then, simple closed-form expressions of some multivariate classical families of polynomials are given. The main advantage of this symbolic representation is the plainness of the setting which reduces to few fundamental statements but also of its implementation in any symbolic software. The role played by cumulants is emphasized within the generalized Hermite polynomials. The new class of multivariate Lévy-Sheffer systems is introduced.File | Dimensione | Formato | |
---|---|---|---|
Oliva_Pre-Print-Multivariate_2012.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
398.22 kB
Formato
Adobe PDF
|
398.22 kB | Adobe PDF | |
Oliva_Multivariate-time-space_2012.pdf
accesso aperto
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
147.29 kB
Formato
Adobe PDF
|
147.29 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.