• 충청수학회지
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• 제6권1호
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• pp.71-87
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• 1993

• 대한수학회지
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• 제35권3호
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• pp.713-725
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• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.383-388
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• 1991

This paper analizes two numerical integration methods, both based on the Runge Kutta 4-th order formula for deterministic systems, for digital simulation of a differential equation driven by white noise. It is shown that a "standard' Runge Kutta method for stochasitic systems yields solutions of Stratonovich differential equations, while Riggs and Phillips' method results in solutions of Ito differential equations. Therefore the white noise differential equation must be converted into the equivalent Ito equation before the latter method is used. Digital simulation results for a simple differential equation are also presented.nted.

• 대한수학회보
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• 제38권1호
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• pp.129-136
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• 2001

We consider a solution process of stochastic differential equation(SDE) driven by S'($R^d$)-valued Wiener process and study a large deviation type of estimates for the process. We get an upper bound in exit probability for such a process to leave a ball of radius $\tau$ before a finite time t. We apply the Ito formula to the SDE under the structure of nuclear space.

• 한국응용과학기술학회지
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• 제31권4호
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• pp.694-702
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• 2014

마이크론 크기를 가지는 ITO(indium tin oxide) 입자들은 인듐과 틴의 수용성 전구체들과 유기 첨가제를 분무 열분해하여 얻었다. 유기 첨가제로서는 에틸렌글리콜과 시트르산을 이용하였다. 분무 열분해 시 에틸렌글리콜과 시트르산과 같은 유기첨가제를 첨가하지 않고 얻어진 ITO 입자들은 구형이며 속이 꽉찬 형태를 가지는데 비해 유기 첨가제를 첨가하여 분무 열분해를 하면 얻어지는 ITO 입자들은 유기 첨가제의 양이 증가 할수록 껍질이 얇고 다공성이 증대된 중공 입자가 얻어진다. 유기첨가제를 첨가하지 않고 분무 열분해를 통해 얻어지는 마이크론 크기를 가지는 ITO는 $700^{\circ}C$에서 두 시간 동안의 후소성과 24 시간동안의 습식 볼밀링에 의해 나노 크기의 ITO로 전환되지 않으나, 유기첨가제를 첨가하고 분무 열분해를 통해 얻어지는 마이크론 크기를 가지는 ITO는 $700^{\circ}C$에서 두 시간 동안의 후소성과 24 시간 동안의 습식 볼밀링에 의해 나노 크기의 ITO로 쉽게 전환되었다. 응집된 나노 크기의 ITO의 일차 입자의 크기를 Debye-Scherrer 식에 의해 계산하였고 ITO 입자를 압축하여 만든 펠렛의 표면저항을 측정하였다.

• Transactions on Electrical and Electronic Materials
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• 제3권2호
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• pp.32-37
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• 2002

This paper gives the basic mechanical properties of indium-tin-oxide (ITO) films on polymer substrates which are exposed to externally and thermally induced bending force. By using modified Storney formula including triple layer structure and bulge test measuring the conductive changes of patterned ITO islands as a function of bending curvature, the mechanical stability of ITO films on polymer substrates was intensively investigated. The numerical analyses and experimental results show thermally and externally induced mechanical stresses in the films are responsible for the difference of thermal expansion between the ITO film and the substrate, and leer substrate material and its thickness, respectively. Therefore, a gradually ramped heating process and an organic buffer layer were employed to improve the mechanical stability, and then, the effects of the buffer layer were also quantified in terms of conductivity-strain variations. As a result, it is uncovered that a buffer layer is also a critical factor determining the magnitude of mechanical stress and the layer with the Young's modulus lower than a specific value can contribute to relieving the mechanical stress of the films.

• 대한수학회지
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• 제41권5호
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• pp.773-793
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• 2004

We consider a system of particles with locations { $X_{i}$ $^{n}$ (t):t$\geq$0,i＝1,…,n} in $R^{d}$ , time-varying weights { $A_{i}$ $^{n}$ (t) : t $\geq$0,i ＝ 1,…,n} and weighted empirical measure processes $V^{n}$ (t)＝1/n$\Sigma$$_{i=1}$$^{n}$ $A_{i}$ $^{n}$ (t)$\delta$ $X_{i}$ $^{n}$ (t), where $\delta$$_{x}$ is the Dirac measure. It is known that there exists the limit of { $V_{n}$ } in the week* topology on M( $R^{d}$ ) under suitable conditions. If { $X_{i}$ $^{n}$ , $A_{i}$ $^{n}$ , $V^{n}$ } satisfies some diffusion equations, applying Ito formula, we prove a central limit type theorem for the empirical process { $V^{n}$ }, i.e., we consider the convergence of the processes η$_{t}$ $^{n}$ ≡ n( $V^{n}$ -V). Besides, we study a characterization of its limit.t.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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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.

• 대한수학회지
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• 제35권3호
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• pp.613-635
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• 1998

In this note we reformulate the white noise calculus on the classical Wiener space (C', C). It is shown that most of the examples and operators can be redefined on C without difficulties except the Hida derivative. To overcome the difficulty, we find that it is sufficient to replace C by L$_2$[0,1] and reformulate the white noise on the modified abstract Wiener space (C', L$_2$[0, 1]). The generalized white noise functionals are then defined and studied through their linear functional forms. For applications, we reprove the Ito formula and give the existence theorem of one-side stochastic integrals with anticipating integrands.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1501-1509
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• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.