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Discrete sampling of functionals of Itô processes

By Emmanuel GOBET and Stéphane Menozzi

Abstract

International audienceFor a multidimensional Ito process $(X_t)_{t \ge 0} $ driven by a Brownian motion, we are interested in approximating the law of $\psi\left((X_s)_{s\in [0,T]}\right)$, $T>0$ deterministic, for a given functional $\psi$ using a discrete sample of the process $X$. For various functionals (related to the maximum, to the integral of the process, or to the killed/stopped path) we extend to the non Markovian framework of Itô processes the results available in the diffusion case. We thus prove that the order of convergence is more specifically linked to the Brownian driver and not to the Markov property of SDEs

Topics: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Publisher: Springer
Year: 2007
DOI identifier: 10.1007/978-3-540-71189-6_19
OAI identifier: oai:HAL:hal-00168857v1
Provided by: Hal-Diderot
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