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Let $C[0,T]$ denote an analogue of Wiener space, the space of real-valued continuous functions on the interval $[0,T]$. For a partition $0=t_0<t_1<\cdots<t_n<t_{n+1}=T$ of $[0,T]$, define $X_n:C[0,T]\to\mathbb R^{n+1}$ by $X_n(x)=(x(t_0),x(t_1),\ldots,x(t_n))$. 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 $X_n$ which has a drift and does not contain the present position of paths. As applications of the formula with $X_n$, we evaluate the Radon-Nikodym derivatives of the functions $\int_0^T[x(t)]^md\lambda(t)(m\in\mathbb N)$ and $[\int_0^Tx(t)d\lambda(t)]^2$ on $C[0,T]$, where $\lambda$ is a complex-valued Borel measure on $[0,T]$. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on $C[0,T]$.
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참고문헌 (11)
참고문헌 신청
R. H. Cameron / 1944 / Transformations of Wiener integrals under transla-tions / Ann. of Math 45(2):386~396
D. H. Cho / 2008 / A simple formula for an analogue of conditional Wiener integrals and its applications / Trans. Amer. Math. Soc 360(7):3795~3811
D. H. Cho / 2009 / A simple formula for an analogue of conditional Wiener integrals and its appli-cations. II / Czechoslovak Math. J 59(2):431~452
D. H. Cho / 2018 / Measurable functions similar to the It^o integral and the Paley-Wiener-Zygmund integral over continuous paths / Filomat 32(18):6441~6456
D. H. Cho / 2019 / An evaluation formula for Radon-Nikodym derivatives similar to conditional expectations over paths / Mathematica Slovaca
D. H. Cho / 2008 / A simple formula for an analogue of conditional Wiener integrals and its applications / Trans. Amer. Math. Soc 360(7):3795~3811
D. H. Cho / 2009 / A simple formula for an analogue of conditional Wiener integrals and its appli-cations. II / Czechoslovak Math. J 59(2):431~452
D. H. Cho / 2018 / Measurable functions similar to the It^o integral and the Paley-Wiener-Zygmund integral over continuous paths / Filomat 32(18):6441~6456
D. H. Cho / 2019 / An evaluation formula for Radon-Nikodym derivatives similar to conditional expectations over paths / Mathematica Slovaca
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