• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.133-146
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• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.585-594
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• 2006

We consider a stochastic integral process represented by multiple Ito-Wiener integrals. We derive gaussian chaos which has some shift continuous function. We get continuity property of self-similar process represented by multiple integrals and finally we show that $Y_{H_t}$ (t) is continuous in t with probability one for Holder function $H_t$ of exponent $\beta$.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.71-87
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• 1993

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.15-22
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• 2013

We find a sufficient condition for optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields studied by Nourdin and Peccati (2009b).

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.303-313
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• 2012

By using the techniques of a Malliavin calculus, we study the asymptotic behavior of the weighted cross-variation of a fractional Brownian sheet with a Hurst parameter $H=(H_1,H_2)$ such that 0 < $H_1$ < 1/2 and 0 < $H_1$ < 1/2.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.851-857
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• 2011

By using Malliavin calculus, we study a central limit theorem of the cross variation related to fractional Brownian sheet with Hurst parameter H = ($H_1$, $H_2$) such that 1/4 < $H_1$ < 1/2 and 1/4 < $H_2$ < 1/2.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.789-799
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• 2007

In this paper, we propose a stochastic finite element formulation which takes into account the randonmess in the material and geometrical parameters. The formulation is proposed for plate structures, and is based on the weighted integral approach. Contrary to the case of elastic modulus, plate thickness contributes to the stiffness as a third-order function. Furthermore, Poisson's ratio is even more complex since this parameter appears in the constitutive relations in the fraction form. Accordingly, we employ Taylor's expansion to derive decomposed stochastic field functions in ascending order. In order to verify the proposed formulation, the results obtained using the proposed scheme are compared with those in the literature and those of Monte Carlo analysis as well.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.5
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• pp.52-59
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• 1996

The boroadband ISDN will transprot the traffics for a wide range of applications with different quality-of-service (QOS) requirements and the priorit control mechanism is an effective method to support multiple classes of services. This paper proposes a new mechanism to satisfy simultaneously the different levels of cell loss performance for the two classes of heterogeneous nonreal-time ATM traffics as well as the delay and loss requirements of real-time traffics. Its performance is analyzed using the stochastic integral approach with the cell arrivals of input streams modeled as markov modulated poisson processes.