Karhunen-Loeve expansion for additive Brownian motions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Liu, Jin V.

关键词: Karhunen-Loeve expansion;    Additive process;    Small deviation;    Laplace transform;   

DOI  :  10.1016/j.spa.2013.06.001

来源: Elsevier

【 摘 要 】

For Gaussian random fields defined as additive processes based on standard Brownian motions and Brownian bridges, we find their Karhunen-Loeve expansions and make connections with related mean centered processes in distribution. Moreover, Pythagorean type distribution identities are established for additive Brownian motions and Brownian bridges. As applications, the corresponding Laplace transform and small deviation estimates are given. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free