On the Karhunen-Loeve expansion for transformed processes

• Autores: Ramón Gutiérrez Jáimez , Mariano José Valderrama Bonnet
• Localización: Trabajos de estadística, ISSN 0213-8190, Vol. 2, Nº. 2, 1987, págs. 81-90
• Idioma: inglés
• DOI: 10.1007/bf02863594
• Títulos paralelos:
  • Sobre el desarrollo de Karhunen-Loeve para procesos transformados
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• Resumen

  • We discuss the influence of the transformation {X(t)} ? {f(t) X(t(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(t(t))} with respect to the measure f-2(t)dt(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process