## Seminar on Probability and Statistics

Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

### 2016/10/31

10:40-11:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Nakahiro Yoshida (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Martingale expansion revisited
[ Abstract ]
The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).