@inbook{7ed3f60b629148219530284232b6341c,
title = "Discrete sampling of functionals of Ito processes",
abstract = "For a multidimensional It{\^o} process (Xt)t ≥ 0 driven by a Brownian motion, we are interested in approximating the law of ω ((Xs)s ∈ [0, T]), T > 0 deterministic, for a given functional φ 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 It{\^o} 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.",
keywords = "Discrete time approximation, Martingale techniques, Non Markovian process",
author = "Emmanuel Gobet and St{\'e}phane Menozzi",
year = "2007",
month = jan,
day = "1",
doi = "10.1007/978-3-540-71189-6\_19",
language = "English",
isbn = "3540711880",
series = "Lecture Notes in Mathematics",
publisher = "Springer Verlag",
pages = "355--374",
booktitle = "Seminaire de Probabilites XL",
}