On the Karhunen-Loeve expansion for transformed processes.

Gutiérrez Jáimez, Ramón, and Valderrama Bonnet, Mariano J.. "On the Karhunen-Loeve expansion for transformed processes.." Trabajos de Estadística 2.2 (1987): 81-90. <http://eudml.org/doc/40503>.

@article{GutiérrezJáimez1987,
abstract = {We discuss the influence of the transformation \{X(t)\} → \{f(t) X(τ(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(τ(t))\} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.},
author = {Gutiérrez Jáimez, Ramón, Valderrama Bonnet, Mariano J.},
journal = {Trabajos de Estadística},
keywords = {Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process},
language = {eng},
number = {2},
pages = {81-90},
title = {On the Karhunen-Loeve expansion for transformed processes.},
url = {http://eudml.org/doc/40503},
volume = {2},
year = {1987},
}

TY - JOUR
AU - Gutiérrez Jáimez, Ramón
AU - Valderrama Bonnet, Mariano J.
TI - On the Karhunen-Loeve expansion for transformed processes.
JO - Trabajos de Estadística
PY - 1987
VL - 2
IS - 2
SP - 81
EP - 90
AB - We discuss the influence of the transformation {X(t)} → {f(t) X(τ(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(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.
LA - eng
KW - Desarrollo en serie de funciones; Aplicaciones; Procesos de Wiener; Movimiento browniano; Gaussian process; Karhunen-Loève expansion; Wiener process; Brownian bridge; Ornstein-Uhlenbeck process
UR - http://eudml.org/doc/40503
ER -