A translation of an analogue of Wiener space with its applications on their product spaces
Commun. Korean Math. Soc. Published online May 13, 2022
Dong Hyun Cho
Abstract : Let $C[0,T]$ denote an analogue of Weiner space, the space of real-valued continuous on $[0,T]$. In this paper, we investigate the translation of time interval $[0,T]$ defining the analogue of Winer space $C[0,T]$. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on $C[0,T]$ as the analogue of Wiener measures on $C[0,s]$ and $C[s,T]$ with $0<s<T$.
Keywords : analogue of Wiener measure, analogue of Wiener space, Brownian motion, Gaussian measure, Wiener measure, Wiener space