• Title, Summary, Keyword: differential equation

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Parameter Estimation for a Hilbert Space-valued Stochastic Differential Equation ?$\pm$

  • Kim, Yoon-Tae;Park, Hyun-Suk
    • Journal of the Korean Statistical Society
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    • v.31 no.3
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    • pp.329-342
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    • 2002
  • We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

Parameter Estimation for an Infinite Dimensional Stochastic Differential Equation

  • Kim, Yoon-Tae
    • Journal of the Korean Statistical Society
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    • v.25 no.2
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    • pp.161-173
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    • 1996
  • When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

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Digital simulation of differential equations driven by white noise (백색잡음 미분방정식에 대한 디지탈 시뮬레이션)

  • 조항주
    • 제어로봇시스템학회:학술대회논문집
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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.

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UNIQUENESS OF SOLUTION FOR IMPULSIVE FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION

  • Singhal, Sandeep;Uduman, Pattani Samsudeen Sehik
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.171-177
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    • 2018
  • In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

THE PARTIAL DIFFERENTIAL EQUATION ON FUNCTION SPACE WITH RESPECT TO AN INTEGRAL EQUATION

  • Chang, Seung-Jun;Lee, Sang-Deok
    • The Pure and Applied Mathematics
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    • v.4 no.1
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    • pp.47-60
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    • 1997
  • In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.

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Stability Analysis of Linear Uncertain Differential Equations

  • Chen, Xiaowei;Gao, Jinwu
    • Industrial Engineering and Management Systems
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    • v.12 no.1
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    • pp.2-8
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    • 2013
  • Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

Web based General Partial Differential Equation Solver using Multidimensional Finite Element Method - I. Model Development - (다차원 유한요소법을 이용한 웹 기반의 범용적 편미분 방정식 해석 모형의 개발 및 적용 - I. 모형의 개발 -)

  • Kim, Joon-Hyun;Han, Young-Han
    • Journal of Environmental Impact Assessment
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    • v.10 no.4
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    • pp.319-326
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    • 2001
  • This study is aimed at the development of a comprehensive web-based partial differential equation solver (WPDES) using multidimensional finite element method, which can be operated on the basis of world wide web. Overall issues of engineering and environmental information management and facility control could be implemented using this solver. This paper describes the development technique of the model, which is first part on development of partial differential equation solver. Conventional commercial general solver of computational fluid dynamics problems were investigated. All the relevant environmental models were analyzed to develop integrated environmental management system using WPDES. The governing equations and the parameters of investigated models were analyzed and integrated. Several numerical modules were invented for each partial differential term in partial differential equation of many related modeling problems. Each module was coded in the fashion of object oriented method, and was combined independently for the overall governing equation. WPDES has unique characteristic, which can analyze the problem through the suitable combination of modules without development of additional models for each environment problem with different governing equation, main variables, and parameters.

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Model Reference Adaptive Control of a Time-Varying Parabolic System

  • Hong, Keum-Shik;Yang, Kyung-Jinn;Kang, Dong-Hunn
    • Journal of Mechanical Science and Technology
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    • v.14 no.2
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    • pp.168-176
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    • 2000
  • Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

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On a direction in the teaching of differential equations (미분방정식 지도에 대한 소고)

  • Park, Jeanam;Jang, Dongsook
    • Communications of Mathematical Education
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    • v.28 no.3
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    • pp.339-352
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    • 2014
  • In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.