• 대한수학회지
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• 제34권4호
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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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• 제33권4호
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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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• 제34권3호
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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.

• 대한수학회보
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• 제34권2호
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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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• 제41권5호
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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.

• 한국지진공학회논문집
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• 제9권6호
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• pp.53-58
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• 2005

본 연구에서는 지진하중을 받는 교량의 거동을 확률밀도함수를 통하여 분석할 수 있는 기법을 개발하였다. 확률밀도함수의 전개는 추계론적 이론을 이용한 반해석적 방법을 통하여 구하였으며, 반해석적 방법은 교량운동방정식으로부터 상응하는 Fokker-Planck equation을 구한 후, path-integral solution을 유도하여 이를 수치적으로 해석함으로써 구할 수 있다. 교량거동의 확률밀도 함수전개로부터 교량거동의 확률적 특성을 파악하고 확률밀도함수의 범위로부터 교량응답거동의 포락선을 얻을 수 있으며 이를 이용하여 최대응답의 범위를 결정할 수 있다는 것을 밝혔다.

• 한국해안해양공학회지
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• 제19권4호
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• pp.303-312
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• 2007

주파수영역에서 쇄파로 인한 에너지 소산에 관한 그 동안의 논쟁은 주파수의 함수인 소산항의 구체적 형태를 중심으로 진행되어왔다. 본 연구에서는 추계학적 쇄파모형과 이에 기초한 스펙트럼으로부터 소산항을 유추하였다. 기존의 인식과는 상이하게 소산항은 주파수의 삼차함수인 것으로 판단된다. 검증작업은 SUPERTANK Laboratory Data Collection Project(Krauss et al., 1992)에서 축적된 실험자료를 기초로 진행되었다. 추가적인 검증을 위해 단조해안에서의 Cnoidal 파랑의 천수과정을 스펙트럼 파랑모형과 제시된 쇄파모형을 차용하여 수치모의하였다. 그 결과 쇄패대역에서 진행되는 파랑의 왜도와 비대칭성의 진화과정이 비교적 정확히 모의되는 성과를 얻었다.

• Bulletin of the Korean Chemical Society
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• 제27권10호
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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.

• 한국물환경학회지
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• 제25권4호
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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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• 제2권3호
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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.