On derivation of random functions from the SFCs by the Ogawa integral (CANCELLED)

2021/01/08 Fri 15:00 - 16:30
Kiyoiki Hoshino
Osaka Prefecture University

(This talk was cancelled.)
We discuss whether and how a random function is identified from its SFCs (short for stochastic Fourier coefficients) induced by the Ogawa integral. In the previous studies, Ogawa, Uemura and the speaker gave affirmative answers for random functions of bounded variation with reconstruction formulas using the law of iterated logarithm for Brownian motion, Kazumi and the speaker gave that for a Skorokhod integral process in the framework of Wiener chaos, and Ogawa and Uemura gave that for certain complex-valued random functions with formulas using the quadratic covariation. In this talk, we introduce the class of random functions which satisfy the desired reconstruction formulas using the quadratic covariation and show regularly Ogawa-integrable random functions including those treated in our previous works are in the class.