Title: Order estimate of functionals related to fBm and asymptotic expansion of variation of fractional SDE
Authors: Hayate Yamagishi - University of Tokyo (Japan) [presenting]
Nakahiro Yoshida - University of Tokyo (Japan)
Abstract: An asymptotic expansion is derived for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals converging to a mixed normal limit. In order to apply the general theory, it is necessary to estimate functionals that are a randomly weighted sum of products of multiple integrals of the fractional Brownian motion, in expanding the quadratic variation and identifying the limit random symbols. To overcome the difficulty, we introduce exponents by means of the weighted graphs capturing the structure of the sum in the functional, and investigate how the exponents change by the action of the Malliavin derivative and its projection.