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.
2012
umbral calculus; multivariate Lévy process; multivariate time-space harmonic polynomial; cumulants
01 Pubblicazione su rivista::01a Articolo in rivista
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.
File allegati a questo prodotto
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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1285558
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact