Abstract
Tangent processes, which are semimartingales with antisymmetric diffusion coefficient, were introduced in the framework of geometry on the path space by Cruzeiro and Malliavin ([3]). They correspond to an extension of the usual Cameron-Martin tangent space in Malliavin calculus, an extension which is in fact necessary in the non-flat situation. In this paper we discuss the possibility of introducing a metric or a Finsler structure on the space of tangent processes. We prove that the Levi—Civita and Cartan connections associated to the natural candidates to the Finsler geometry are not well defined.
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References
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Cruzeiro, A.B., Xiang, KN. (2003). On Metrics for Tangent Processes on the Path Space. In: Çapar, U., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VIII. Progress in Probability, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8020-6_4
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DOI: https://doi.org/10.1007/978-3-0348-8020-6_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9406-7
Online ISBN: 978-3-0348-8020-6
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