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The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes

Published online by Cambridge University Press:  01 July 2016

Ushio Sumita  and
Masaaki Kijima
Ushio Sumita
Affiliation:
University of Rochester
Masaaki Kijima*
Affiliation:
University of Rochester
*
∗Postal address: The Graduate School of Management, The University of Rochester, Rochester, NY 14627, USA.
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Abstract

In the study of bivariate processes, one often encounters expressions involving repeated combinations of bivariate continuum operations such as multiple bivariate convolutions, marginal convolutions, tail integration, partial differentiation and multiplication by bivariate polynomials. In many cases numerical computation of such results is quite tedious and laborious. In this paper, the bivariate Laguerre transform is developed which provides a systematic numerical tool for evaluating such bivariate continuum operations. The formalism is an extension of the univariate Laguerre transform developed by Keilson and Nunn (1979), Keilson et al. (1981) and Keilson and Sumita (1981), using the product orthonormal basis generated from Laguerre functions. The power of the procedure is proven through numerical exploration of bivariate processes arising from correlated cumulative shock models.

Keywords

BIVARIATE FUNCTIONSGENERALIZED FOURIER SERIESMULTIPLE BIVARIATE CONVOLUTIONSTAIL INTEGRATIONPARTIAL DIFFERENTIATIONBIVARIATE AND MARGINAL MOMENTSCORRELATED CUMULATIVE SHOCK MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 4 , December 1985 , pp. 683 - 708
Copyright
Copyright © Applied Probability Trust 1985 

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