Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(5): 1531-1548

Online first article August 25, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150795

Copyright © The Korean Mathematical Society.

Change of scale formulas for a generalized conditional Wiener integral

Dong Hyun Cho and Il Yoo

Kyonggi University, Yonsei University

Abstract

Let $C[0,t]$ denote the space of real-valued continuous functions on $[0,t]$ and define a random vector $Z_n:C[0,t]\to\mathbb R^n$ by $Z_n(x)=(\int_0^{t_1}h(s) dx(s),\ldots,\int_0^{t_n}h(s) dx(s))$, where $0

Keywords: analogue of Wiener space, change of scale formula, conditional Wiener integral, simple formula for conditional Wiener integral, Wiener measure

MSC numbers: Primary 28C20, 60G05, 60G15, 60H05