Karhunen-Loève expansion for a generalization of Wiener bridge

Matyas Barczy, Rezső L. Lovas

We derive a Karhunen-Loève expansion of the Gauss process $B_t-g(t){\int }_0^1{g}^{\prime }(u)d{B}_u$, $t\in [0,1]$, where $(B_t{)}_{t\in [0,1]}$ is a standard Wiener process and $g:[0,1]\to R$…