Alili, Larbi and Wu, Ching-Tang (2009) Further results on some singular linear stochastic differential equations. Stochastic Processes and their Applications, Vol.119 (No.4). pp. 1386-1399. doi:10.1016/j.spa.2008.07.004 ISSN 0304-4149.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title:	Stochastic Processes and their Applications
Publisher:	Elsevier Science BV
ISSN:	0304-4149
Official Date:	April 2009
Dates:	Date Event April 2009 Published
Volume:	Vol.119
Number:	No.4
Number of Pages:	14
Page Range:	pp. 1386-1399
DOI:	10.1016/j.spa.2008.07.004
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Austrian Science Foundation (FWF), National Science Council Taiwan
Grant number:	Z36-MAT, NSC 96-2115-M-009-005-MY2

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