• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.23-40
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• 2023

This paper is concerned by the controllability results of impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, Krasnoselkii fixed point method and the theory of resolvent operator in the sense of Grimmer. A practical example is provided to illustrate the viability of the abstract result of this work.

• 한국통신학회논문지
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• 제28권2A호
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• pp.63-69
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• 2003

본 논문에서는 몬테칼로 유한차분 시간영역 해석법을 이용하여 프랙탈 형상을 가진 완전 도체 표면에서 산란된 장을 구하였다. 프랙탈 형상을 가진 1차원 표면은 프랙셔널 브라운 모션 모델을 사용하여 생성하였다. 프랙탈 표면의 형상을 결정하는 스펙트럼 변수(S0), 프랙탈 차원(D)에 대한 역방향 산란계수를 계산하였다. 계산에 사용된 표면의 수는 80개, 표면의 점의 수는 1024개이고, 표면의 길이는 16파장이었다. 계산된 결과의 타당성을 검증하기 위해 소 섭동 근사기법을 이용하여 계산된 결과와 비교하였다. 그 결과 양자간의 결과는 서로 잘 일치함을 알 수 있었다.

• 대한수학회지
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• 제38권3호
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• pp.577-594
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• 2001

In this paper we establish limit theorems on the large and small increments of a two-parameter Gaussian random process on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter Gaussian random process.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.1-10
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• 2015

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

• 대한수학회지
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• 제46권2호
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• pp.347-361
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• 2009

In this paper, by estimating small ball probabilities of $l^{\infty}$-valued Gaussian processes, we investigate Chung-type law of the iterated logarithm of $l^{\infty}$-valued Gaussian processes. As an application, the Chung-type law of the iterated logarithm of $l^{\infty}$-valued fractional Brownian motion is established.

• 한국정보통신학회논문지
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• 제23권4호
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• pp.416-422
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• 2019

본 논문은 절차적함수를 이용하여 실시간으로 3차원 구름을 모델링하고 렌더링하는 알고리즘을 제안한다. 구름 모델링은 절차적 노이즈 함수인 fbm(Fractional Brownian Motion)을 변형하여 사용하며, 이 값을 대기의 수증기 밀도 값으로 이용한다. 이 밀도 값은 파라미터로 주어진 3가지 구름의 형태를 위해 변형되며 렌더링단계의 입력 값으로 들어간다. 레이마칭(ray marching)기법을 이용한 렌더링 단계에서는 이 밀도 값을 이용하여 구름의 색상을 결정하며 이때 밀도에 따른 빛의 감소 및 산란현상은 물리적으로 계산된다. 대기모델로 렌더링 된 하늘 위에 제안한 알고리즘에 의해 구현된 구름들이 블랜딩되며, 이 때 바람의 방향에 따라 구름이 움직이도록 한다. 제안된 구름 생성 및 렌더링은 GLSL언어를 이용해서 GPU상에서 구현되었다.

• Communications for Statistical Applications and Methods
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• 제22권3호
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• pp.277-283
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• 2015

Pickands constant $H_{\alpha}$ appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of $H_{\alpha}$ is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of $H_{\alpha}$. In this paper, we attempt to compute numerically $H_{\alpha}$ based on its representation derived by $H{\ddot{u}}sler$ (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture $H_{\alpha}=1/{\Gamma}(1/{\alpha})$ for 0 < ${\alpha}$ ${\leq}$ 2. This conjecture does not seem compatible with our simulation result for 1 < ${\alpha}$ < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2006년도 춘계 학술발표회 논문집
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• pp.179-188
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• 2006

In this study, R/S analysis which was proposed by Mandelbrot & Wallis(1969) was applied to evaluate the presence of the fractal property in the cone tip resistance of in-situ CPT data. Hurst exponents(H) were evaluated in the range of $0.660\sim0.990$ and the average was 0.875. It was confirmed that a cone tip resistance data had the characteristic of fractals and it was expected that cone tip resistance data sets are well approximated by a fBm process with an Hurst exponent near 0.875. It was also observed that the boundary between layers were obviously identified as a result of R/S analysis and it will be usage in practices.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1995년도 춘계학술대회
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• pp.37-41
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• 1995

In this paper, we proposed the 2-stage ultrasound liver image classifier which uses the fractal dimensions obtained from the original image and its 1/2 subsampled image, and the Normalized Fourier Power Spectrum. The fractal dimension based on Fractional Brownian Motion (FBM) is calculated from the variance of the same scale pixels instead of the mean of them. Since the actual ultrasound. liver images does not fully match the FBM, to get the fractal dimension, we use the scale vectors which satisfy the FBM model. In 2-stage classifier, we first classified normal and diffuse liver and then classified the fat liver and cirrhosis from the diffuse liver. For the test liver images. 70% of normal liver and 80% of fat liver and 90% of cirrhosis is classified classified with our 2-stage classifier.

• 천문학회보
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• 제39권1호
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• pp.59.2-59.2
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• 2014

Radiative transfer models in a spherical, turbulent interstellar medium (ISM), in which the photon source is situated at the center, are calculated to investigate the correlation between the scattered light and the dust column density. The medium is modeled using fractional Brownian motion structures that are appropriate for turbulent ISM. The correlation plot between the scattered light and optical depth shows substantial scatter and deviation from simple proportionality. It was also found that the overall density contrast is smoothed out in scattered light. In other words, there is an enhancement of the dust-scattered flux in low-density regions, while the scattered flux is suppressed in high-density regions. The correlation becomes less significant as the scattering becomes closer to being isotropic and the medium becomes more turbulent. Therefore, the scattered light observed in near-infrared wavelengths would show much weaker correlation than the observations in optical and ultraviolet wavelengths. We also find that the correlation plot between scattered lights at two different wavelengths shows a tighter correlation than that of the scattered light versus the optical depth.