On the Karhunen-Loeve expansion for transformed processes
ISSN: 0213-8190
Año de publicación: 1987
Volumen: 2
Número: 2
Páginas: 81-90
Tipo: Artículo
Otras publicaciones en: Trabajos de estadística
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