Abstract
Based on the norm in the Hilbert Space , 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.
Citation
Yongchun Zhou. Xiaohui Ai. Minghao Lv. Boping Tian. "Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/457051