• Title, Summary, Keyword: Brownian motion

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ESTIMATION OF DRIFT PARAMETER AND CHANGE POINT VIA KALMAN-BUCY FILTER FOR LINEAR SYSTEMS WITH SIGNAL DRIVEN BY A FRACTIONAL BROWNIAN MOTION AND OBSERVATION DRIVEN BY A BROWNIAN MOTION

  • Mishra, Mahendra Nath;Rao, Bhagavatula Lakshmi Surya Prakasa
    • 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.

MEAN DISTANCE OF BROWNIAN MOTION ON A RIEMANNIAN MANIFOLD

  • Kim, Yoon-Tae;Park, Hyun-Suk
    • Proceedings of the Korean Statistical Society Conference
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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.

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The Analysis of the Stock Price Time Series using the Geometric Brownian Motion Model (기하브라우니안모션 모형을 이용한 주가시계열 분석)

  • 김진경
    • 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.

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A Distribution for Regulated ${\mu}-Brownian$ Motion Process with Control Barrier at $x_{0}$

  • Park, Young-Sool
    • 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 ${\mu}-RBMPx_{0}$.

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A Distribution of Terminal Time Value and Running Maximum of Two-Dimensional Brownian Motion with an Application to Barrier Option

  • Lee, Hang-Suck
    • Proceedings of the Korean Statistical Society Conference
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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.

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A NOTE ON FUNCTIONAL LIMIT THEOREM FOR THE INCREMENTS OF FBM IN SUP-NORM

  • Hwang, Kyo-Shin
    • 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.

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Effective Bandwidth for a Single Server Queueing System with Fractional Brownian Input

  • Kim, Sung-Gon;Nam, Seung-Yeob;Sung, Dan-Keun
    • Proceedings of the Korean Statistical Society Conference
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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.

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Some Limit Theorems for Fractional Levy Brownian Motions on Rectangles in the Plane

  • Hwang, Kyo-Shin;Kang, Soon-Bok;Park, Yong-Kab;Jeon, Tae-Il;Oh, Ho-Seh
    • 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.

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