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Further results on some singular linear stochastic differential equations

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  • Alili, Larbi
  • Wu, Ching-Tang

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.

Suggested Citation

  • Alili, Larbi & Wu, Ching-Tang, 2009. "Further results on some singular linear stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1386-1399, April.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1386-1399
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    References listed on IDEAS

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    1. Deheuvels, Paul, 1982. "Invariance of Wiener processes and of Brownian bridges by integral transforms and applications," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 311-318, September.
    2. Baudoin, Fabrice, 0. "Conditioned stochastic differential equations: theory, examples and application to finance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 109-145, July.
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    Cited by:

    1. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.

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