Papers by Carlos Bárcenas
Applied Stochastic Models and Data Analysis, 1992
The utility of the classical Karhunen-Loève expansion of a second order process is limited to its... more 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.
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Papers by Carlos Bárcenas