Further results on some singular linear stochastic differential equations
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.
Year of publication: |
2009
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Authors: | Alili, Larbi ; Wu, Ching-Tang |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 119.2009, 4, p. 1386-1399
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Publisher: |
Elsevier |
Keywords: | Brownian motion Canonical decomposition Enlargement of filtrations Goursat kernels Gramian matrices Self-reproducing kernels Stochastic differential equations Volterra transform |
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