Markov-modulated Lévy processes lead to matrix integral equations of the kind A0 + A1X + A2X2 + A3(X) = 0, where A0, A1, A2 are given matrix coefficients, while A3(X) is a nonlinear function, expressed in terms of integrals involving the exponential of the matrix X itself. In this paper we propose some numerical methods for the solution of this class of matrix equations, perform a theoretical convergence analysis, and show the effectiveness of the new methods by means of a wide numerical experimentation. © 2022 Society for Industrial and Applied Mathematics.
Numerical Solution of a Matrix Integral Equation Arising in Markov-Modulated Lévy Processes
Bini, Dario;Latouche, Guy;Meini, Beatrice
2022-01-01
Abstract
Markov-modulated Lévy processes lead to matrix integral equations of the kind A0 + A1X + A2X2 + A3(X) = 0, where A0, A1, A2 are given matrix coefficients, while A3(X) is a nonlinear function, expressed in terms of integrals involving the exponential of the matrix X itself. In this paper we propose some numerical methods for the solution of this class of matrix equations, perform a theoretical convergence analysis, and show the effectiveness of the new methods by means of a wide numerical experimentation. © 2022 Society for Industrial and Applied Mathematics.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
mmlp_rev.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
546.49 kB
Formato
Adobe PDF
|
546.49 kB | Adobe PDF | Visualizza/Apri |
bini_latouche_meini_SISC2022.pdf
non disponibili
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - accesso privato/ristretto
Dimensione
569.58 kB
Formato
Adobe PDF
|
569.58 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.