• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.49-59
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• 2001

In this paper we introduce the modified conditional Yeh-Wiener integral. To do so, we first treat the modified Yeh-Wiener integral. And then we obtain the simple formula for the modified conditional Yeh-Wiener integral and valuate the modified conditional Yeh-Wiener integral for certain functional using the simple formula obtained. Here we consider the functional using the simple formula obtained. Here we consider the functional on a set of continuous functions which are defined on various regions, for example, triangular, parabolic and circular regions.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.627-635
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• 2001

In this paper, we first introduce the modified Yeh-Wiener integral and then consider the modified conditional Yeh-Wiener integral. Here we use the space of continuous functions on a different region which was discussed before. We also evaluate some modified conditional Yeh-Wiener integral with examples using the simple formula for the modified conditional Yeh-Wiener integral.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.811-815
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.809-822
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.419-439
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• 1999

In this paper, we first develop a general formula for evaluating conditional abstract Wiener integrals of cylinder functions. we next use our formula to evaluate the conditional abstract wiener integral of various cylinder functions and then specialize our results to conditional Yeh-Wiener integrals to show that we can obtain the corresponding results by Park and Skoug. We finally obtain a Cameron-Martin translation theorem for conditional abstract Wiener integrals.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.65-72
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• 2000

In this paper we treat the Yeh-Wiener integral and the conditional Yeh-Wiener integral for vector-valued conditioning function which are examples of the function space integrals. Finally, we state the modified conditional Yeh-Wiener integral for vector-valued conditioning function.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.489-494
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• 2016

The purpose of this paper is to treat the generalized conditional Yeh-Wiener integral for the sample path-valued conditioning function. As a special case of our results, we obtain the results in [6].

• The Journal of Natural Sciences
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• v.11 no.1
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• pp.1-5
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• 1999

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.