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5 avril 2022


Séminaire ANR EFFI

Programme :

9h15-10h15, Nakahiro Yoshida, Université de Tokyo, Asymptotic expansion of variations.

Abstract: We discuss some recent developments in the theory of asymptotic expansion and their applications to variations. Beyond the traditional theory for mixing processes in ergodic statistics, the theory of asymptotic expansion is extending to non-ergodic statistics. Nualart and Yoshida (2019 EJP) presented asymptotic expansion for Skorohod integrals.  The method of random symbols in Yoshida (2013 SPA) for martingales with a mixed normal limit was used to specify the asymptotic expansion formula of a Skorohod integral.  With this machinery, moreover, we obtain asymptotic expansion of a randomly weighted quadratic variation of a fractional Brownian motion. Asymptotic expansion for a variation of a Brownian motion with anticipative weights is also discussed. A notion of exponent is introduced to assess the effect of various random polynomials of multiple Wiener integrals appearing in the stochastic expansion of the variation (Yoshida 2020 arXiv).

10h30-11h30, Marina Kleptsyna, Le Mans Université, Estimation of the Hurst parameter from continuous noisy data.

Abstract: This talk addresses estimation problem for the Hurst parameter of the fractional Brownian motion from noisy continuous time data. Consistent estimation in this setup is possible only if either the length of the observation interval increases to infinity or intensity of the noise decreases to zero. The main result is a proof of local asymptotic normality (LAN) in each of these asymptotic regimes, which reveals the optimal minimax rates. Joint work with Pavel Chigansky (University of Jerusalem).


Dans le cadre du projet ANR 2022-2026 « Efficient inference for large and high-frequency data"


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