統計数学セミナー

過去の記録 ~02/05次回の予定今後の予定 02/06~

担当者 吉田朋広、荻原哲平、小池祐太
セミナーURL http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/
目的 確率統計学およびその関連領域に関する研究発表, 研究紹介を行う.

2017年04月20日(木)

15:00-   数理科学研究科棟(駒場) 117号室
David Nualart 氏 (Kansas University) -
Central limit theorem for symmetric integrals
[ 講演概要 ]
The purpose of this talk is to present the convergence in distribution of symmetric integrals of functions of the fractional Brownian motion for critical values of the Hurst parameter. This result includes the cases of symmetric integrals defined as the limit of trapeziodal, midpoint and Simpson Riemann sums, where the corresponding critical values of the Hurst parameter are H=1/4, H=1/6 and H=1/10, respectively. As a consequence, we establish a change-of-variable formula in law, where the correction term involves a stochastic integral with respect to an independent standard Brownian motion. The proof is based on the combination of Malliavin calculus and the classical Bernstein's big blocks/small blocks technique.
David Nualart 氏 (Kansas University) -
Stochastic heat equation with rough multiplicative noise
[ 講演概要 ]
The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.