• 대한수학회보
• /
• 제59권5호
• /
• pp.1093-1103
• /
• 2022

In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces (H, B, 𝜈). To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in 𝓛(B), the Banach space of bounded linear operators from B to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in 𝓛(B). We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.

• 대한수학회논문집
• /
• 제21권1호
• /
• pp.117-133
• /
• 2006

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a generalized Fresnel class $F_{A1,A2}$ containing the Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space. In this paper, we present a change of scale formula for Wiener integrals of various functions on $B^2$ which need not be bounded or continuous.

• 대한수학회보
• /
• 제57권3호
• /
• pp.751-762
• /
• 2020

We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.

• 대한수학회보
• /
• 제53권3호
• /
• pp.903-924
• /
• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• 전자공학회논문지D
• /
• 제35D권6호
• /
• pp.8-14
• /
• 1998

Wiener-Hopf 적분방정식으로부터 경계면 위의 전체파를 미지수로 하는 파수영역에서의 쌍적분 방정식을 얻는 기존의 유도과정을 검토하였다. 이러한 기존의 유도 과정은 결국 Wiener-Hopf 적분방정식으로부터 Helmholtz-Kirchhoff 적분방정식을 유도하는 과정임을 해석적으로 보였다.

• 호남수학학술지
• /
• 제30권4호
• /
• pp.723-732
• /
• 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
• /
• 제28권4호
• /
• pp.615-622
• /
• 2015

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

• 충청수학회지
• /
• 제30권1호
• /
• pp.67-76
• /
• 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.

• 대한수학회논문집
• /
• 제13권4호
• /
• pp.811-815
• /
• 1998

In this paper we define a sample path-valued conditional Yeh-Wiener integral for function F of the type E[F(x)$\mid$x(*,(equation omitted))=$\psi({\blacktriangle})]$, where $\psi$ is in C[0, (equation omitted)] and ${\blacktriangle}$ = (equation omitted) and evaluate a sample path-valued conditional Yeh-Wiener integral using the result obtained.

• 대한수학회보
• /
• 제36권4호
• /
• pp.809-822
• /
• 1999

In this paper, we introduce conditional Yeh-Wiener in-tegrals for generalized conditioning functions including vector-valued functions. And also we establish various evaluation formulas of conditional Yeh-Wiener integrals for generalized conditioning functions.