• 대한수학회논문집
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• 제37권3호
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• pp.749-763
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• 2022

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.

• 충청수학회지
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• 제26권4호
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• pp.735-742
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• 2013

In this note, we prove the translation theorem for the generalized analogue of Wiener measure space and we show some properties of the generalized analogue of Wiener measure from it.

• 대한수학회보
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• 제47권1호
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• pp.131-149
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• 2010

In 1992, the author introduced the definition and the properties of Wiener measure over paths in Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.

• 호남수학학술지
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• 제29권4호
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• pp.577-588
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• 2007

Bearman's rotation theorem is not only very important in pure mathematics but also plays the key role for various research areas, related to Wiener measure. In 2002, the author and professor Im introduced the concept of analogue of Wiener measure, a kind of generalization of Wiener measure and they presented the several papers associated with it. In this article, we prove a formula on analogue of Wiener measure, similar to the formula in Bearman's rotation theorem.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.317-333
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• 2007

In 2002, the author and professor Ryu introduced the concept of analogue of Wiener measure. In this paper, we prove the existence theorem of Fourier-Feynman transform on analogue of Wiener measure in $L_2-norm$ sense.

• 호남수학학술지
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• 제30권4호
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• pp.723-732
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• 2008

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

• 충청수학회지
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• 제30권1호
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• pp.67-76
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• 2017

In this note, we prove the theorems in the generalized analogue of Wiener space corresponding to the second and the third arcsine laws in either concrete or analogue of Wiener space [1, 2, 7] and we show that our results are exactly same to either the concrete or the analogue of Wiener case when the initial condition gives either the Dirac measure at the origin or the probability Borel measure.

• 충청수학회지
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• 제22권3호
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• pp.579-586
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• 2009

Let $\varphi$ be a complete probability measure on $\mathbb{R}$, let $m_{\varphi}$ be the analogue of Wiener measure over paths on [0, T] and let f(t) be continuously differentiable on [0, T]. In this note, we give the analogue of Wiener measure $m_{\varphi}$ of {x in C[0, T]$\mid$x(0) < f(0) and $x(s_0){\geq}f(s_{0})$ for some $s_{0}$ in [0, T]} by use of integral equation techniques. This result is a generalization of Park and Paranjape's 1974 result[1].

• 충청수학회지
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• 제23권1호
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• pp.119-126
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• 2010

In this paper, we find the formula for the analogue of Wiener measure over the subset of C[0, T] bounded by the sectionally differentiable functions, which is a generalization of Park and Skoug's results in [2].

• 충청수학회지
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• 제23권4호
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• pp.711-720
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• 2010

In this note, we will establish the integration formulae for functionals such as $F(x)=\prod_{j=1}^{n}\;x(s_j)^2$ and $G(x)=\exp\{{\lambda}{\int}_{0}^{t}\;x(s)^2dm_L(s)\}$ in the analogue of Wiener measure space and using our formulae, we will derive some formulae for series.