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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{align*} 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{align*} 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 $[0,T]$.
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참고문헌 (12)
참고문헌 신청
R. H. Cameron / 1980 / Analytic functions / Springer
C. C. Chen / 1992 / Principles and Techniques in Combinatorics / World Scientific Publishing Co., Inc
Dong Cho / 2018 / Measurable functions similar to the itô integral and the Paley-Wiener-Zygmund integral over continuous paths / Filomat 32(18):6441~6456
Dong Hyun Cho / 2021 / An Evaluation Formula for Radon–Nikodym Derivatives Similar to Conditional Expectations over Paths / Bulletin of the Malaysian Mathematical Sciences Society 44(1):203~222
조동현 / 2020 / A Banach algebra and its equivalent spaces over paths with a positive measure / 대한수학회논문집 35(3):809~823
C. C. Chen / 1992 / Principles and Techniques in Combinatorics / World Scientific Publishing Co., Inc
Dong Cho / 2018 / Measurable functions similar to the itô integral and the Paley-Wiener-Zygmund integral over continuous paths / Filomat 32(18):6441~6456
Dong Hyun Cho / 2021 / An Evaluation Formula for Radon–Nikodym Derivatives Similar to Conditional Expectations over Paths / Bulletin of the Malaysian Mathematical Sciences Society 44(1):203~222
조동현 / 2020 / A Banach algebra and its equivalent spaces over paths with a positive measure / 대한수학회논문집 35(3):809~823
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