• 대한수학교육학회지:학교수학
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• 제17권1호
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• pp.1-18
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• 2015

본 연구는 2009 개정 교육과정에서 그 중요성이 강조되었으며 새로운 2015 교육과정의 개정에서 확대 적용이 예상되는 수학적 과정이 수학 교과서에 구현된 정도를 확인하고 그 내용에 있어서 보완이 요구되는 요소를 추출하는 것을 목적으로 한다. 이를 위해 2009 개정 수학과 교육과정의 수학적 과정과 미국의 CCSSM의 수학적 실천의 비교를 통해 공통 요소와 차이나는 요소를 파악함으로써 우리나라 학교수학에 추가적으로 필요한 수학적 과정 요소를 탐색하고, 현행 초등학교 4학년 수학 교과서를 대상으로 수학적 과정에 있으나 구현되지 않은 수학적 실천 요소 또는 수학적 과정이 아니지만 구현된 수학적 실천 요소에 대해서 분석하였다. 각각에 대한 분석 결과를 제시하고, 그에 따른 논의로부터 교육과정 개정 및 수학 교과서 개발시 수학적 과정의 보완 및 구현을 위한 시사점을 제안한다.

• 대한수학회지
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• 제37권1호
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• pp.45-53
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• 2000

Existence of a unique invariant probability is considered for a class of Markov processes which may not be irreducible and a functional central limit theorem for a class of nonlinear irreducible uniformly ergodic processes is derived as well.

• 대한수학회보
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• 제35권4호
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• pp.837-845
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• 1998

In this work, we consider Euler approxiamtion for one-dimensional jump-diffusion processes under Yamada-Watanabe type conditions on the coefficients which turns out to converge to the strong solution in uniform $L^1$-sense.

• 대한수학회지
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• 제35권1호
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• 대한수학회지
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• 제56권4호
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• 대한수학회보
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• 제54권2호
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• pp.573-581
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• 2017

Reflected Ornstein-Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. In this work, we are concerned with the study of asymptotic behaviours of parametric estimation for ergodic reflected Ornstein-Uhlenbeck processes with two-sided barriers. Moreover, we also focus on the relations between regulators and the local time process.

• 대한수학회논문집
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• 제12권4호
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• pp.1033-1038
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• 1997

A functional central limit theorem for a class of nonlinear stationary Markov processes which are geometrically Harris ergodic is derived.

• 대한수학회논문집
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• 제10권4호
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• pp.963-974
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• 1995

We formulate central limit theorems for non-linear functionals of stationary Gaussian vector processes with long-range dependence.

• 대한수학회지
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• 제37권1호
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• pp.1-19
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• 2000

We formulate a non-central limit theorem for non-linear functionals of stationary Gaussian vector processes with dependence.

• 충청수학회지
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• 제12권1호
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• pp.119-124
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• 1999

In this paper, T.Kawata's result[2] is generalized, by means of Hausdorff-Young inequality and Beurling's norm.