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On the numerical expansion of a second order stochastic process

Author

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  • Ramón Gutiérrez
  • Juan Carlos Ruiz
  • Mariano J. Valderrama

Abstract

The utility of the classical Karhunen‐Loève expansion of a second order process is limited to its practical derivation, because it depends upon the solution of a Fredholm integral equation associated with it whose kernel is the covariance function of the process. So, in this paper we study two numerical procedures for solving such equations, the Rayleigh‐Ritz and the collocation methods, and also essay two different bases of L2‐orthogonal functions in order to perform the algorithms, Legendre polynomials and trigonometric functions, on two well‐known processes, the Wiener‐Lévy process and the Brownian‐bridge. The accuracy of the numerical results in relation to the real ones, as well as comparative studies among both procedures are also included.

Suggested Citation

  • Ramón Gutiérrez & Juan Carlos Ruiz & Mariano J. Valderrama, 1992. "On the numerical expansion of a second order stochastic process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 8(2), pages 67-77, June.
    • Handle: RePEc:wly:apsmda:v:8:y:1992:i:2:p:67-77
    DOI: 10.1002/asm.3150080202
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    Cited by:

    1. Ruiz-Molina, Juan Carlos & Navarro, Jesús & Valderrama, J. Mariano, 1999. "Differentiation of the modified approximative Karhunen-Loeve expansion of a stochastic process," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 91-98, March.

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