Intertwinned Diffusions by Examples
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.
KeywordsLinear and equi-variant connections stochastic differential equations geometry of diffusion operators
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This article is based on the books [11, 13] and could and should be considered as joint work with K.D. Elworthy and Y. LeJan and I would like to thank them for helpful discussions. However, any short comings and errors are my sole responsibility. This research is supported by an EPSRC grant (EP/E058124/1).
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