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Intertwinned Diffusions by Examples

In: Stochastic Analysis 2010

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  • Xue-Mei Li

    (University of Warwick, Mathematics Institute)

Abstract

We discuss the geometry induced by pairs of diffusion operators on two states spaces related by a map from one space to the other. This geometry led us to an intrinsic point of view on filtering. This will be explained plainly by examples, in local coordinates and in the metric setting. This article draws largely from the books (“Elworthy et al., On the geometry of diffusion operators and stochastic flows, Lecture Notes in Mathematics 1720, Springer, 1999”, “Elworthy et al., The Geometry of Filtering. To appear in Frontiers in Mathematics Series, Birkhauser”) and aims to have a comprehensive account of the geometry for a general audience.

Suggested Citation

  • Xue-Mei Li, 2011. "Intertwinned Diffusions by Examples," Springer Books, in: Dan Crisan (ed.), Stochastic Analysis 2010, pages 51-71, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-15358-7_4
    DOI: 10.1007/978-3-642-15358-7_4
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