• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1019-1028
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• 1997

The integral solution for a deterministic evolution equation was introduced by Benilan. Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic evolution euation under some conditions for the coefficients. Moreover we prove that this solution is a unique strong solution.

• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.459-470
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• 2004

We study the approximation of the solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H > 1/2 through discretization of space and time. The rate of convergence of an approximation for Euler scheme is established.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.197-208
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• 2005

We consider the problem for approximate solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter $H\;\in$ (0,1/2). The error of the approximate solution for the explicit Euler scheme is investigated.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.233-245
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• 1997

In this paper, we study the asymptotic behavior of a random evolution. Some examples of random evolution can be found in Chapter 12 of [2].

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.53-58
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• 2005

Semi-analytical methodology to examine the dynamic responses of a bridge is developed via the joint probability density function. The evolution of joint probability density function is evaluated by the semi-analytical procedure developed. The joint probability function of the bridge responses can be obtained by solving the path-integral solution of the Fokker-Planet equation corresponding to the stochastic differential equations of the system. The response characteristics are observed from the joint probability density function and the boundary of the envelope of the probability density function can provide the maxima ol the bridge responses.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.4
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• pp.303-312
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• 2007

There is still a controversy going on about how to model energy dissipation due to breaking over frequency domain. In this study, we unveil the exact structure of energy dissipation using stochastic wave breaking model. It turns out that contrary to our present understanding, energy dissipation is cubically distributed over frequency domain. The verification of proposed model is conducted using the acquired data during SUPERTANK Laboratory Data Collection Project (Krauss et al., 1992). For further verification, we numerically simulate the nonlinear shoaling process of Conoidal wave over a beach of uniform slope, and obtain very promising results from the viewpoint of a skewness and asymmetry of wave field, usually regarded as the most fastidious parameter to satisfy.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Journal of Korean Society on Water Environment
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• v.25 no.4
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• pp.507-514
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• 2009

In this study, a dynamic modeling scheme is presented to describe the probabilistic structure of soil water and plant water stress index under stochastic precipitation conditions. The proposed model has the form of the Fokker-Planck equation, and its applicability as a model for the probabilistic evolution of the soil water and plant water stress index is investigated under a climate change scenario. The simulation results of soil water confirm that the proposed soil water model can properly reproduce the observations and show that the soil water behaves with consistent cycle based on the precipitation pattern. The simulation results of plant water stress index show two different PDF patterns according to the precipitation. The simple impact assessment of climate change to soil water and plant water stress is discussed with Korean Meteorological Administration regional climate model.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.3
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• pp.119-126
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• 2010

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.