English

Further results on some singular linear stochastic differential equations

Probability 2008-05-29 v2

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.

Keywords

Cite

@article{arxiv.math/0702785,
  title  = {Further results on some singular linear stochastic differential equations},
  author = {Larbi Alili and Ching-Tang Wu},
  journal= {arXiv preprint arXiv:math/0702785},
  year   = {2008}
}