• 대한수학회보
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• 제37권3호
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• pp.619-631
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• 2000

We study a class of catalytic super Brownian motion X in 1-dimension. We show under some conditions of catalyst, the process X is absolutely continuous and we get a stochastic partial differential equation for X.

• 한국대기환경학회:학술대회논문집
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• 한국대기환경학회 2003년도 춘계학술대회 논문집
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• pp.355-356
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• 2003

Coagulation is a process whereby particles collide with one another due to their relative motion, and adhere to form large particles. Coagulation caused by the random Brownian motion of particles is called Brownian coagulation. Many properties, such as light scattering, electrostatic charges, toxicity, as well as physical processes, including diffusion, condensation and thermophoresis depend strongly on their size distribution. Therefore, Brownian coagulation is substantially important in atmospheric science, combustion technology, inhalation toxicology and nuclear safety analysis. (omitted)

• Communications for Statistical Applications and Methods
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• 제28권3호
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• pp.251-265
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• 2021

This paper discusses the pricing of autocallable structured product with knock-in (KI) feature using the exit probability with the Brownian Bridge technique. The explicit pricing formula of autocallable ELS derived in the existing paper handles the part including the minimum of the Brownian motion using the inclusion-exclusion principle. This has the disadvantage that the pricing formula is complicate because of the probability with minimum value and the computational volume increases dramatically as the number of autocall chances increases. To solve this problem, we applied an efficient and robust simulation method called the Brownian Bridge technique, which provides the probability of touching the predetermined barrier when the initial and terminal values of the process following the Brownian motion in a certain interval are specified. We rewrite the existing pricing formula and provide a brief theoretical background and computational algorithm for the technique. We also provide several numerical examples computed in three different ways: explicit pricing formula, the Crude Monte Carlo simulation method and the Brownian Bridge technique.

• 문화기술의 융합
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• 제4권3호
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• pp.159-163
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• 2018

본 연구는 인간의 서사의 브라운운동을 생리학적 관점으로 서술한다. 그리고 이러한 기능이 문학작품에 어떻게 나타나는지를 살펴서 향후 문학치료의 시행에 활용할 목적을 지니고 있다. 황진이 시조는 처음에 그리움을 베어내는 행위를 한다. 그리고 다음에 그 그리움을 접어 보관을 한다. 마지막으로 그 그리움을 펼쳐내는 것이다. 이렇게 접고 펼침의 운동으로 이 시조는 진동한다. 이것이 시조의 브라운운동이라고 할 수 있다. 이로써 끝없는 사랑을 완성한다. 이러한 문학적 감정의 브라운운동을 활용한다면, 문학치료가 인체생리학적인 치유의 조건들을 형성할 수 있을 것으로 사료된다.

• 한국가시화정보학회지
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• 제3권1호
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• pp.3-19
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• 2005

Novel optical techniques are presented for three-dimensional tracking of nanoparticles; Optical Serial Sectioning Microscopy (OSSM) and Ratiometric Total Internal Reflection Fluorescent Microscopy (R-TIRFM). OSSM measures optically diffracted particle images, the so-called Point Spread Function (PSF), and dotermines the defocusing or line-of-sight location of the imaged particle measured from the focal plane. The line-of-sight Brownian motion detection using the OSSM technique is proposed in lieu of the more cumbersome two-dimensional Brownian motion tracking on the imaging plane as a potentially more effective tool to nonintrusively map the temperature fields for nanoparticle suspension fluids. On the other hand, R-TIRFM is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth of an argon-ion laser is used to provide a thin illumination field of an order of a few hundred nanometers from the wall. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.477-491
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• 2021

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.71-84
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• 2014

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H = 1/4.

• 대한수학회논문집
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• 제11권2호
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• pp.471-480
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• 1996

Consider a strong Markov process $X^0$ that has continuous sample paths in the closed cone $\bar{G}$ in $R^d(d \geq 3)$ such that the process behaves like a ordinary Brownian motion in the interior of the cone, reflects instantaneously from the boundary of the cone and is absorbed at the vertex of the cone. It is shown that $X^0(t)$ has a representation $R(t) \ominus (t)$ where $R(t) \in [0, \infty)$ and $\ominus(t) \in S^{d-1}$, the surface of the unit ball.

• Journal of the Korean Data and Information Science Society
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• 제22권3호
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• pp.549-553
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• 2011

In this paper, we deal with the problem of deciding the length of data for estimating the parameters in geometric Brownian motion. As an approach to this problem, we consider the change point test and introduce simple test statistic based on the cumulative sum of squares test (cusum test). A real data analysis is performed for illustration.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.