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The Bivariate Laguerre Transform and Its Applications: Numerical Exploration of Bivariate Processes

Ushio Sumita and Masaaki Kijima
Advances in Applied Probability
Vol. 17, No. 4 (Dec., 1985), pp. 683-708
DOI: 10.2307/1427083
Stable URL: http://www.jstor.org/stable/1427083
Page Count: 26
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The Bivariate Laguerre Transform and Its Applications: Numerical Exploration of Bivariate Processes
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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.

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