• 대한수학회지
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• 제38권2호
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• pp.297-309
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• 2001

White noise distribution theory over the complex Gaussian space is established on the basis of the recently developed white noise operator theory. Unitarity condition for a white noise operator is discussed by means of the operator symbol and complex Gaussian integration. Concerning the overcompleteness of the exponential vectors, a coherent sate representation of a white noise function is uniquely specified from the diagonal coherent state representation of the associated multiplication operator.

• 충청수학회지
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• 제29권2호
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• 대한수학회지
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• 제33권3호
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• 대한수학회지
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• 제33권4호
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.825-834
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• 2013

In this paper, we study the Yeh convolution of white noise functionals. We first introduce the notion of Yeh convolution of test white noise functionals and prove a dual property of the Yeh convolution. By applying the dual object of the Yeh convolution, we study the Yeh convolution of generalized white noise functionals, which is a non-trivial extension. Finally, we study relations between the Yeh convolution and Fourier-Gauss, Fourier-Mehler transform.

• 대한수학회지
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• 제35권3호
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• pp.793-802
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• 1998

We apply the generalization of Levy's infinitesimal equation $\delta$X(t) = $\psi$(X(s), s $\leq$ t, $Y_{t}$, t, dt), $t\in R^1$, for a random field X (C) indexed by a contour C or by a more general set. Assume that the X(C) is homogeneous in x, say of degree n, then we can appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X (C.)

• Communications for Statistical Applications and Methods
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• 제17권1호
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• pp.47-54
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• 2010

By using the white noise theory for fractional Brownian sheet, we give new representations of the Wick integrals of various types with respect to fractional Brownian sheet with Hurst parameters $H_1,H_2{\in}$(0, 1).

• 충청수학회지
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• 제23권1호
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• pp.1-10
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• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.

• 한국정보시스템학회지:정보시스템연구
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• 제14권2호
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• pp.257-276
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• 2005

This study adopts diffusion of innovation theory and analyses product life cycle on two different information communication technology (ICT) products. One is telematics located on introduction and the other one is MP3 located on maturity. The analytical results were mixed. ordinary least square (OLS) result showed that adoption of MP3 player is affected by white noise error ($\varepsilon$) and telematics is influenced by innovation effect (p coefficient) rather than imitation effect (q coefficient) or white noise error. However, nonlinear least square (NLS) result showed that adoption of MP3 player is affected by imitation effect (q coefficient) rather than innovation effect (p coefficient). In addition, the ratio of imitation effect/innovation effect of MP3 player is larger than that of telematics.

• 대한수학회보
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• 제51권3호
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• pp.847-862
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• 2014

Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. Error estimates are established for the fully coupled optimality system using Brezzi-Rappaz-Raviart theory. Numerical examples are also presented to examine our theoretical results.