- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 A generalized simple formula for evaluating Radon-Nikodym derivatives over paths J. Korean Math. Soc.Published online September 22, 2020 Dong Hyun Cho Kyonggi University Abstract : Let $C[0,T]$ denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval $[0,T]$. Define $Z_{\vec e,n}:C[0,T]\to\mathbb R^{n+1}$ by \begin{eqnarray*} Z_{\vec e,n}(x)=\left(x(0),\int_0^Te_1(t)dx(t),\ldots,\int_0^Te_n(t)dx(t)\right), \end{eqnarray*} where $e_1, \ldots,e_n$ are of bounded variations on $[0,T]$. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on $C[0,T]$ with the conditioning function $Z_{\vec e,n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on $C[0,T]$ which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval $[0,T]$. Keywords : analogue of Wiener measure, Banach algebra, conditional Wiener integral, cylinder function, Feynman integral, Wiener integral, Wiener space MSC numbers : 28C20,60G05,60G15 Full-Text :