• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.120-126
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• 2011

The fatigue damages in structural details of offshore plants can be accumulated due to various environmental loadings such as swell, wave, wind and current. It is known that load histories acting on mooring and riser systems show stationary and ergodic bimodal wide-banded process. This paper provides refined approach to obtain time signals representing stress range histories from wide-banded bimodal spectrum which consists of ideally narrow-banded and fully separated two spectrums. Variations of the probabilistic characteristics for time signals according to frequency and sampling time increments are compared with the reference data to be the probabilistic characteristics such as zero-crossing period, peak period, and irregularity factor obtained from an assumed ideal spectrum. It is proved that the sampling time increment more affects on the probabilistic characteristics than frequency increment. The fatigue damages according to the frequency and sampling time increments are also compared with the ones with minimum increment condition which are thought to be exact fatigue damage. It is concluded that the maximum sampling time increment to obtain reliable time signals should be determined that ratio of applied maximum sampling time increment and minimum period is less than approximately 0.08.

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.123-131
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• 2000

Let {X(t) : t $\geq$B 0} be a Symmetric $\alpha$ Stable and H-Self-similar process with stationary increments. We examine a.s. Holder unboundedness of S$\alpha$S H-sssi Chentsov processes and H-sssi Chentsov fields for order ${\gamma}$>H. Finally, we prove a.s. Holder continuity of S$\alpha$S H-sssi processes with ergodic seating transformations for the case of H>1/$\alpha$.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.194-200
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• 1995

The baker's transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting begavior of the partial sum process of a martingale sequence constructed from the baker's transformation in the context of an invariance principle of a uniform central limit theorm.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.983-990
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• 2006

In this paper, we study an asymmetric power fractionally integrated GARCH model and find a region on which the process is stationary ergodic and has long memory property.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.499-501
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• 1994

Let ${X_n}$ be conditionally i.i.d. given $g \subset \sigma(X_n, n \geq 1)$. We will prove that $g$ is degenerate if and only if ${X_n, n \geq 1}$ are i.i.d. random variable(r.v.s). As a corollary the Hewitt-Savage zero-one law is obtained using the fact that interchageable process is conditionally i.i.d. given the $\sigma$-algebra of permutable events.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.409-417
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• 1995

We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1067-1076
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• 2017

This paper considers the asymptotic behaviors of the processes generated by the classical ergodic tent map that is defined on the unit interval. We develop a sequential empirical process and get the uniform version of law of iterated logarithm for the tent map by using the bracketing entropy method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.3C
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• pp.243-250
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• 2009

In this paper, a closed-form expression of the ergodic channel capacity for a narrow-band time-reversal communication scheme is analytically formulated. In the time-reversal communication scenario, a transmitter sends a signal and a so-called time-reversal array receives the signal. Then, the received signal is reversed in the time do main and resent to the original transmitter. Here, one transmitter and an antenna array for the time-reversal array are assumed. Since the spacing between the array elements is large, the signals received by each antenna element can be considered independent. For simplicity, the communication channel is assumed stationary, whose properties are not changed for the time-reversal process. Based on the obtained formulation, the channel capacities for the time-reversal and the conventional channels are compared.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.267-280
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• 2007

In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.