Asymptotic expansion and estimates of Wiener functionals

Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and other random symbols. To specify these random symbols, it is necessary to classify the level of the effect of each term appearing in the stochastic expansion of the variable in question. To solve this problem, we consider a class L of certain sequences (In)n is an element of N of Wiener functionals and give a systematic way of estimation of the order of (In)n is an element of N. Based on this method, we introduce a notion of exponent of the sequence (In)n is an element of N, and investigate the stability and contraction effect of the operators Dun and D on L, where un is the integrand of a Skorohod integral. After constructed these machineries, we derive asymptotic expansion of the variation having anticipative weights. An application to robust volatility estimation is mentioned.(c) 2022 Published by Elsevier B.V.