• 대한수학회논문집
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• 제20권1호
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• pp.135-144
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• 2005

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

• 대한수학회보
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• 제44권4호
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• 대한수학회보
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• 제40권1호
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• 대한수학회지
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• 제50권1호
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• pp.41-59
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• 2013

In this paper, we investigate the existence and controllability results for a class of abstract stochastic evolution differential inclusions with nonlocal conditions where the linear part is nondensely defined and satisfies the Hille-Yosida condition. The results are obtained by using integrated semigroup theory and a fixed point theorem for condensing map due to Martelli.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 하계학술대회 논문집 B
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• pp.901-903
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• 1995

The ordinary differential equation (ODE) method has been widely used for the convergence analysis of stochastic recursive algorithms. The principal objective of this method is to associate to a given algorithm a differential equation with continuous righthand side. Usually some assumptions should be imposed to get such a differential equation. If any of assumptions fails, then the ODE method cannot be used. Recently a new method using differential inclusions (DIs) was introduced in [3], which is useful to deal with those cases. The DI method shares the same idea with the ODE method, but it is different in that a differential inclusion is identified instead of a differential equation with continuous righthand side. In this paper, we briefly review the DI method and then analyze a Robbins and Monro (RM)-type algorithm. Our focus is placed on the projected algorithm.

• KDI Journal of Economic Policy
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• 제36권3호
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• pp.1-23
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• 2014

본고는 4개의 거시변수들을 포함한 Time Varying VAR 모형을 통해 한국의 통화정책 변화를 평가하였다. 첫째, 외환위기나 금융위기 때와 같이 통화정책이 환율변동에 대해 민감하게 변화하는 시기가 존재하므로 위기를 포함한 긴 표본 안에서 한국의 통화정책을 평가할 때는 환율을 모형안에 포함시키는 것이 필요하다. 둘째, 표본기간 내에서 이례적인 큰 변동성이 때때로 나타나는 한국 거시변수들을 설명하기 위해서는 stochastic volatilities를 TVP-VAR 모형 내에서 설정할 필요가 있다. 한편, 2000년대 거시변수들의 안정화는 stochastic volatilities의 감소에 의해 설명되며, 부분적으로는 거시경제의 구조를 반영하는 충격반응함수에 의해서도 설명된다. 셋째, 통화정책의 인플레이션에 대한 유효성의 크기는 예전에 비해 최근 약화된 편이나 유효성의 지속성은 비교적 높아진 것으로 나타났다. 마지막으로 인플레이션 안정화에 대한 통화정책의 기조는 물가안정목표제가 도입되기 전에 비해 그 후에 적극적인 방향으로 개선되어 왔음을 보이고 있다. 하지만 우리나라의 통화정책은 그 기조가 경기변동에 비해 인플레이션 안정화에 대하여 여전히 덜 적극적인 것을 감안할 때 개선될 여지가 있는 것으로 판단된다.

• 대한수학회보
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• 제55권6호
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• pp.1691-1701
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• 2018

New inclusion sets are obtained for the eigenvalues of real matrices for which the all 1's vector is an eigenvector, i.e., the constant row-sum real matrices. A number of examples are provided. This paper builds upon the work of the authors in [7]. The results of this paper are in terms of $Ger{\check{s}}gorin$ discs of the second type. An application of the main theorem to bounding the algebraic connectivity of connected simple graphs is obtained.

• Structural Engineering and Mechanics
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• 제57권2호
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• pp.369-387
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• 2016

In this work, random homogenization analysis for the effective thermal properties of a three-dimensional composite material with unidirectional fibers is presented by combining the equivalent inclusion method with Random Factor Method (RFM). The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters are completely accounted for, and stochastic effective thermal properties as thermal expansion coefficients as well as their correlation are then sought. Results from the RFM and the Monte-Carlo Method (MCM) are compared. The impact of randomness and correlation of the micro-structural parameters on the random homogenized results is revealed by two methods simultaneously, and some important conclusions are obtained.

• 지구물리와물리탐사
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• 제7권1호
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• pp.14-18
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• 2004

High levels of ambient noise and safety factors often limit the use of 'active-source' seismic methods for geotechnical investigations in urban environments. As an alternative, shear-wave velocity-depth profiles can be obtained by treating the background microtremor wave field as a stochastic process, rather than adopting the traditional approach of calculating velocity based on ray path geometry from a known source. A recent field test in Melbourne demonstrates the ability of the microtremor method, using only Rayleigh waves, to resolve a velocity inversion resulting from the presence of a hard, 12 m thick basalt flow overlying 25 m of softer alluvial sediments and weathered mudstone. Normally the presence of the weaker underlying sediments would lead to an ambiguous or incorrect interpretation with conventional seismic refraction methods. However, this layer of sediments is resolved by the microtremor method, and its inclusion is required in one-dimensional layered-earth modelling in order to reproduce the Rayleigh-wave coherency spectra computed from observed seismic noise records. Nearby borehole data provided both a guide for interpretation and a confirmation of the usefulness of the passive Rayleigh-wave microtremor method. Sensitivity analyses of resolvable modelling parameters demonstrate that estimates of shear velocities and layer thicknesses are accurate to within approximately $10\%\;to\;20\%$ using the spatial autocorrelation (SPAC) technique. Improved accuracy can be obtained by constraining shear velocities and/or layer thicknesses using independent site knowledge. Although there exists potential for ambiguity due to velocity-thickness equivalence, the microtremor method has significant potential as a site investigation tool in situations where the use of traditional seismic methods is limited.

• 한국수산과학회지
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• 제34권1호
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• pp.43-50
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• 2001

규칙파, 불규칙파 및 파랑과 흐름이 공존하는 상태에서 프레임에 우리형 그물을 부착하여 구성되어 있는 가두리 시설의 운동특성을 분석하기 위하여 정사각형 및 원형 구조의 가두리 시설을 대상으로 예인 수조에서 수리 모형실험을 실시하였으며, 규칙파중 운동 특성은 선형 포텐셜 이론에 의한 수치 해석의 그것과 비교하였다. 그 결과는 다음과 같이 요약할 수 있다. 1) 규칙파중 모형 가두리 시설의 상하 및 종 동요는 전후 동요와는 달리 그물의 영향을 거의 받지 않았으므로 이 시설물의운동 특성중 가장 중요한 상하 동요를 해석하는 경우에는 그물을 제외하고 프레임만을 고려해도 된다는 것을 확인하였다. 2) 불규칙파중 및 파랑과 흐름이 공존하는 상태에서 모형 가두리 시설의 운동 특성은 입사파 주기의 2배 되는 고주파수에서 시설물의 고유 주기 등에 의해 동적 운동의 peak frequency가 나타남으로써 비선형 즉, 2nd order harmonic 성분이 존재하였다 3) 파동 및 흐름장에서 동요 특성이 정사각형에 비해 비교적 작게 나타난 원형이 파도, 조류 등 환경 조건이 거친 해역에 보다 적합한 것으로 판단되었다.