• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1063-1073
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• 2018

We study the estimation of the drift parameter and the change point obtained through a Kalman-Bucy filter for linear systems with signal driven by a fractional Brownian motion and the observation driven by a Brownian motion.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.317-333
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• 1998

In this study, I employed the autoregressive model and the geometric Brownian motion model to analyze the recent stock prices of Korea. For all 7 series of stock prices(or index) the geometric Brownian motion model gives better predicted values compared with the autoregressive model when we use smaller number of observations.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.197-208
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• 2005

We consider the problem for approximate solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter $H\;\in$ (0,1/2). The error of the approximate solution for the explicit Euler scheme is investigated.

• East Asian mathematical journal
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• v.24 no.3
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• pp.275-287
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• 2008

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.73-78
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• 2003

This presentation derives a distribution function of the terminal value and running maximum of two-dimensional Brownian motion {X(t) = (X$_1$(t), X$_2$(T))', t > 0}. One random variable of the joint distribution is the terminal time value of the Brownian motion {X$_1$(t), t > 0}. The other random variable is the partial-time running maximum of the Brownian motion {X$_2$(t), t > 0}. With this distribution function, this presentation also derives an explicit pricing formula for a barrier option whose monitoring period of the option starts at an arbitrary date and ends at another arbitrary date before maturity.

• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.1-8
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• 2003

The traffic patterns of today's IP networks exhibit two important properties: self-similarity and long-range dependence. The fractional Brownian motion is widely used for representing the traffic model with the properties. We consider a single server fluid queueing system with input process of a fractional Brownian motion type. Formulas for effective bandwidth are derived in a single source and multiple source cases.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.1-19
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• 1999

In this paper we establish some limit theorems for a two-parameter fractional Levy Brownian motion on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter fractional Levy Brownian motion.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.545-561
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• 2003

We use the first-passage-time formulation by Torquato, Kim and Cule ［J. Appl. Phys., Vol. 85, pp. 1560∼1571 (1999) ］, which makes use of the first-passage region in association with the diffusion tracer's Brownian movement, and develop a new efficient Brownian motion simulation method to compute the effective conductivity of digitized composite media. By using the new method, one can remarkably enhance the speed of the Brownian walkers sampling the medium and thus reduce the computation time. In the new method, we specifically choose the first-passage regions such that they coincide with two, four, or eight digitizing units according to the dimensionality of the composite medium and the local configurations around the Brownian walkers. We first obtain explicit solutions for the relevant first-passage-time equations in two-and three-dimensions. We then apply the new method to solve the illustrative benchmark problem of estimating the effective conductivities of the checkerboard-shaped composite media. for both periodic and random configurations. Simulation results show that the new method can reduce the computation time about by an order of magnitude.