 Asymptotic expansion and estimates of Wiener functionalsNakahiro Yoshida Stochastic Processes and their Applications, 2023, vol. 157, issue C, 176-248 Abstract: 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∈N of Wiener functionals and give a systematic way of estimation of the order of (In)n∈N. Based on this method, we introduce a notion of exponent of the sequence (In)n∈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. Keywords: Asymptotic expansion; Variation; Mixed normal distribution; Malliavin calculus; Random symbol; Exponent; Watanabe’s delta functional; Compact group (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:157:y:2023:i:c:p:176-248 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.10.003 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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