• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.227-234
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• 1998

Criteria are derived for the existence of a unique invariant oprobability distribution of a class of nonlinear pth-order autoregressive oprocesses, which reformulate those of Tweedie's. It will be shown that the criteria in this paper are easily applicable to the linear or piecewise linear case so that some of the earlier results are immediate consequences of our main results.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1033-1038
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• 1997

A functional central limit theorem for a class of nonlinear stationary Markov processes which are geometrically Harris ergodic is derived.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.607-613
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• 2007

Eigenstructure assignment provides the advantage of allowing great flexibility in shaping the closed-loop system responses by allowing specification of closed-loop eigenvalues and corresponding eigenvectors. But, the general eigenstructure assignment methodologies cannot guarantee stability robustness to parameter variations of a system. In this paper, we present a novel method that has the capability of exact assignment of an eigenstructure which can consider the probability of instability for LTI (Linear Time-Invariant) systems. The probability of instability of an LTI system is determined by the probability distributions of the closed-loop eigenvalues. The stability region for the system is made probabilistically based upon the Monte Carlo evaluations. The proposed control design method is applied to design a flight control system with probabilistic parameter variations to confirm the usefulness of the method.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.261-265
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• 2017

Let X and Y be independent identically distributed nondegenerate random variables with common absolutely continuous probability distribution function F(x) and the corresponding probability density function f(x) and $E(X^2)$<${\infty}$. Put Z = max(X, Y) and W = min(X, Y). In this paper, it is proved that Z - W and Z + W or$(X-Y)^2$ and X + Y are independent if and only if X and Y have normal distribution.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1117-1122
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• 1996

A class of nonlinear Markov processes on the real line is considered, and a functional central limit theorem is proved for the functions of bounded variation on the real line by identifying a broad subset of the range of the generator.

• 전기의세계
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• v.29 no.11
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• pp.742-750
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• 1980

The problem of nonlinear time-invariant system identification by estimation of Wiener kernels is studied for discrete time systems with inputs having symmetric probability distributions. G-functionals are constructed. It is further shown that under idealized conditions, these seemingly different techniques yield the same results. The results of identification of asimulated second degree system is presented.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.30 no.5
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• pp.365-372
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• 2019

We propose a method to estimate unknown parameters(e.g., target amplitude and clutter parameters) in the generalized likelihood ratio test(GLRT) using maximum likelihood estimation and the Newton-Raphson method. When detecting targets in a clutter environ- ment, it is important to establish a modular model of clutter similar to the actual environment. These correlated clutter models can be generated using spherically invariant random vectors. We obtain the GLRT of the generated clutter model and check its detection probability using estimated parameters.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.4
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• pp.467-474
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• 2004

A large-eddy simulation is performed for turbulent flow in a concentric annulus with the inner wall rotation at Re$\sub$Dh/=8900 for three rotation rates N=0.2145, 0.429 and 0.858. Main emphasis is placed on the inner wall rotation effect on near-wall turbulent structures. Near-wall turbulent structures close to the inner wall are scrutinized by computing the lower-order statistics. The anisotropy invariant map for the Reynolds stress tensor and the invariant function are illustrated to reveal the altered anisotropy in turbulent structure. Probability density functions of the splat/anti-splat process are explored to develop a sufficiently complete picture of the contributions of the flow events to turbulent production. The present numerical results show that the altered turbulent structures may be attributed to the centrifugal instability, which leads to the augmentation of sweep and ejection events.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2660-2669
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• 1996

In this paper, it is called nonlinear-symbol CPFSK(NCPFSK) which is modulated by the nonlinear function of information carrying phase function within all symbol interval produce time invariant trellis structure. In general, the bit error probability performance of CPFSK modultion scheme within given signal constellation is determined from the number of memory elementsof continuous phase encoder, i.e. number of state. In this paper the number of state of analyticall designed NCPFSK is time invariant. And the nonlinear symbol mapping function of the proposed moudlation produces the nonlinear symbol andthe phase state of the modulation for updating the phase function of NCPFSK. It si shown in this paper nonlinear symbol CPFSK with multiple TCM to make further improvements in d$^{2}$, and analyzed BER performance in AWGN channel envioronments.hannel envioronments.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.427-446
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• 1995

Let S be a set and B be a $\sigma$-field on S. We consider $(\Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $\Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = \cdots, X_-1, X_0, X_1, \cdots$ the coordinate maps on $\Omega$. From our assumptions it follows that ${X_i}_{i \in Z}$ is a stationary and ergodic process.