Föllmer–Dirichlet Processes

Francesco Russo,Pierre Vallois

doi:10.1007/978-3-031-09446-0_14

Föllmer–Dirichlet Processes

Francesco Russo, Pierre Vallois

https://doi.org/10.1007/978-3-031-09446-0_14

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Publication Date: Jan 1, 2022

Affiliation: Institut Polytechnique de Paris, École Nationale Supérieure de Techniques Avancées, Institut Élie Cartan de Lorraine, Université de Lorraine

#Quadratic Variation Process #Bessel Process + Show 8 more

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Abstract

AbstractAn important class of finite quadratic variation processes is the one of (Föllmer–)Dirichlet processes which are the sum of a local martingale and a zero quadratic variation process. An interesting example is the one of Lyons–Zheng processes which are the generalizations of time-reversible semimartingales in the class of Dirichlet processes. A Bessel process in low dimension is not a semimartingale, nevertheless it is a Lyons–Zheng process. We revisit the Bouleau–Yor formula which extends Itô-Tanaka formula to the case of non-convex functions of semimartingales.

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