Abstract
Nualart and Yoshida (2019) presented a general scheme for asymptotic expansion of Skorohod integrals. However, when applying the general theory to a variation of a process related to a fractional Brownian motion, one repeatedly needs estimates of the order of Lp-norms and Sobolev norms of functionals that are complicated as a randomly weighted sum of products of multiple integrals of the fractional Brownian motion. To resolve the difficulties, in this paper, we construct a theory of exponents based on a graphical representation of the structure of the functionals, which enables us to tell an upper bound of the order of functionals by a simple rule. We also show how the exponents change by the actions of the Malliavin derivative and its projection. The exponents are useful in various studies of limit theorems as well as in applications to asymptotic expansion.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
