Further results on some singular linear stochastic differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Alili, Larbi¹  Wu, Ching-Tang² 

[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

[2] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 300, Taiwan

关键词: Brownian motion;    Canonical decomposition;    Enlargement of filtrations;    Goursat kernels;    Gramian matrices;    Self-reproducing kernels;    Stochastic differential equations;    Volterra transform;   

DOI  :  10.1016/j.spa.2008.07.004

来源: Elsevier

【 摘 要 】

A class of Volterra transforms, preserving the Wiener measure, with kernels of Goursat type is considered. Such kernels satisfy a self-reproduction property. We provide some results on the inverses of the associated Gramian matrices which lead to a new self-reproduction property. A connection to the classical reproduction property is given. Results are then applied to the study of a class of singular linear stochastic differential equations together with the corresponding decompositions of filtrations. The studied equations are viewed as non-canonical decompositions of some generalized bridges. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free