Abstract
Classical contact geometry is an odd-dimensional analogue of symplectic geometry. We show that a natural probabilistic deformation of contact geometry, compatible with the very irregular trajectories of diffusion processes, allows one to construct the stochastic version of a number of basic geometrical tools, like, for example, Liouville measure. Moreover, it provides an unified framework to understand the origin of explicit relations (cf. “quadrature”) between diffusion processes, useful in many fields. Various applications are given, including one in stochastic finance.
The present paper resulted from a visit of the first author at the GFMUL (Lisbon) within the project POCTI/MAT/34924/2000. Both authors are grateful to the Ascona’s organizers for the opportunity to present their results.
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Lescot, P., Zambrini, JC. (2007). Probabilistic Deformation of Contact Geometry, Diffusion Processes and Their Quadratures. In: Dalang, R.C., Russo, F., Dozzi, M. (eds) Seminar on Stochastic Analysis, Random Fields and Applications V. Progress in Probability, vol 59. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8458-6_12
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DOI: https://doi.org/10.1007/978-3-7643-8458-6_12
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