Further results on some singular linear stochastic differential equations

Details Further results on some singular linear stochastic differential equations Further results on some singular linear stochastic differential equations

2007-02-26

arxiv.org/abs/math/0702785v2

Mathematics

Probability

Scientific paper

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.

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