Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion

الملخص EN

Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace.

Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge.

As applications, Laplace transform, large deviation, and small deviation are given.