• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.411-420
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• 2013

We consider fractional Gussian noise and FARIMA sequence with Gaussian innovations and show that the suitably scaled distributions of the FARIMA sequences converge to fractional Gaussian noise in the sense of finite dimensional distributions. Finally, we figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, $d$, 0) by using R/S method.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.365-382
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• 2023

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noise by using the Picard-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.8B
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• pp.667-680
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• 2008

In this work, we present the results of our empirical study on 802.11 wireless LAN network traffic. We collect the packet trace from existing campus wireless LAN infra-structure. We analyzed four different data sets: aggregate traffic, upstream traffic, downstream traffic, tcp only packet trace from aggregate traffic. We analyze the time series aspect of underlying traffic (byte count process and packet count process), marginal distribution of time series, and packet size distribution. We found that in all four data sets there exist long-range dependent property in byte count and packet count process. Inter-arrival distribution is well fitted with Pareto distribution. Upstream traffic, i.e. from the user to Internet, exhibits significant difference in its packet size distribution from the rests. Average packet size of upstream traffic is 151.7 byte while average packet size of the rest of the data sets are all greater than 260 bytes. Packets with full data payloads constitutes 3% and 10% in upstream traffic and the downstream traffic, respectively. Despite the significant difference in packet size distribution, all four data sets have similar Hurst values. The Hurst alone does not properly explain the stochastic characteristics of the underlying traffic. We model the underlying traffic using fractional-ARIMA (FARIMA) and fractional Gaussian Noise (FGN). While the fractional Gaussian Noise based method is computationally more efficient, FARIMA exhibits superior performance in accurately modeling the underlying traffic.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.25-25
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• 2023

The ensemble optimal interpolation (EnOI) scheme is a sub-optimal alternative to the ensemble Kalman filter (EnKF) with a reduced computational demand making it potentially more suitable for operational applications. Since only one model is integrated forward instead of an ensemble of model realizations, online estimation of the background error covariance matrix is not possible in the EnOI scheme. In this study, we investigate two Gaussian noise based ensemble generation strategies to produce dynamic covariance matrices for assimilation of water level observations into a distributed hydrological model. In the first approach, spatially correlated noise, sampled from a normal distribution with a fixed fractional error parameter (which controls its standard deviation), is added to the model forecast state vector to prepare the ensembles. In the second method, we use an adaptive error estimation technique based on the innovation diagnostics to estimate this error parameter within the assimilation framework. The results from a real and a set of synthetic experiments indicate that the EnOI scheme can provide better results when an optimal EnKF is not identified, but performs worse than the ensemble filter when the true error characteristics are known. Furthermore, while the adaptive approach is able to reduce the sensitivity to the fractional error parameter affecting the first (non-adaptive) approach, results are usually worse at ungauged locations with the former.

• The KIPS Transactions:PartC
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• v.11C no.5
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• pp.621-632
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• 2004

Recent measurement studies of real teletraffic data in modern telecommunication networks have shown that self-similar (or fractal) processes may provide better models of teletraffic in modern telecommunication networks than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A new generator of pseu-do-random self-similar sequences, based on the fractional Gaussian nois and a wavelet transform, is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results by better matching the self-similar structure of long range dependent processes, than other types of wavelets. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is 0(n).

• ETRI Journal
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• v.26 no.6
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• pp.635-640
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• 2004

A new low-complexity differential detection technique, fractional multi-bit differential detection (FMDD), is proposed in order to improve the performance of continuous phase modulation (CPM) signals such as Gaussian minimum shift keying (GMSK) and Gaussian frequency shift keying (GFSK). In comparison to conventional one-bit differential detected (1DD) GFSK, the FMDD-employed GFSK provides a signal-to-noise ratio advantage of up to 1.8 dB in an AWGN channel. Thus, the bit-error rate performance of the proposed FMDD is brought close to that of an ideal coherent detection while avoiding the implementation complexity associated with the carrier recovery. In the adjacent channel interference environment, FMDD achieves an even larger SNR advantage compared to 1DD.

• The Journal of the Acoustical Society of Korea
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• v.16 no.5
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• pp.96-104
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• 1997

In this paper, we proposed new methods for estimation of time delay and time-frequency delay in impulsive noise environment. The proposed methods are developed using the theory of ${\alpha}-stable$ distribution, including the fractional negative order moment(FNOM) and minimum dispersion(MD), which are formulated for the time delay estimation and the fractional negative order ambiguity function and complex minimum dispersion, which are difined for the joint estimation of time delay and frequency delay. Through simulation work, its performance was compared with various other algorithms. As a result, while the conventional approaches based on second-order statistics are only verified in Gaussian noise environent ($S{\alpha}S$ noise with ${\alpha}$=2) and also the recently proposed robust methods by Nikias[7] are verified only in limited impulse noise ($S{\alpha}S$ noise with the range of $1<{\alpha}{\le}2$), the methods proposed are able to estimate the time delay in Gaussian and any impulsive noise environments($S{\alpha}S$ noise with the range of $0<{\alpha}{\le}2$).

• Journal of the Korean Society for Precision Engineering
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• v.18 no.9
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• pp.71-81
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• 2001

This paper analyzes the effectiveness of minimizing vibration and sound transmission on/through a thin rectangular plate by both feedback control and hybrid control which combines adaptive feedforward control with a feedback loop. An experimental system identification technique using the matrix-fractional curve-fitting of the frequency response data is introduced for complex shaped structures. This identification technique reduces the model order o the MIMO(Multi-Input Multi-Output) system which simplifies the practical implementation. The adaptive feedforward control uses a Multiple filtered-x LMS(Least Mean Square) algorithm and the feedback control uses a multivariable digital LQG(Linear Quadratic Gaussian) algorithm. Experimental results show that an effective reduction of sound transmission is achieved by the hybrid control scheme when both vibration and noise measurement signals are incorporated in the controller.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.1
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• pp.269-286
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• 2018

Signal detection in symmetric alpha-stable ($S{\alpha}S$) distributed noise is a challenging problem. This paper proposes a detector based on a decreasing exponential function (DEF). The DEF detector can effectively suppress the impulsive noise and achieve good performance in the presence of $S{\alpha}S$ noise. The analytical expressions of the detection and false alarm probabilities of the DEF detector are derived, and the parameter optimization for the detector is discussed. A performance analysis shows that the DEF detector has much lower computational complexity than the Gaussian kernelized energy detector (GKED), and it performs better than the latter in $S{\alpha}S$ noise with small characteristic exponent values. In addition, the DEF detector outperforms the fractional lower order moment (FLOM)-based detector in $S{\alpha}S$ noise for most characteristic exponent values with the same order of magnitude of computational complexity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.9 no.3
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• pp.115-124
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• 1997

We measured the variance of eddy diffusion and associated ‘diffusion coefficients’ in coastal regions of Korea by observing the separation distances among multiple drifters deployed simultaneously at the same initial position. The variance of eddy diffusion was found to be proportional to $t^m$, where t is the time and m is a non-integer scaling exponent between 1.5 and 3.5. The observed scaling exponent of eddy diffusion cannot be reproduced by diffusion models employing constant eddy diffusivity. In this study, we applied fractal theory in simulating exponential increase of variance of eddy diffusion. We employed the fGn(fractional Gaussian noise) as a ‘modified’ random walks corresponding to the oceanic eddy diffusion. The variance of eddy diffusion, which corresponds to the fBm(fractional Brown motion) of our diffusion model, is proportional to $t^{2H}$, where H is Hurst scaling exponent. The temporal increase of the variance. with scaling exponent between 1 and 2, was successfully reproduced by our fractal diffusion model. However, our model cannot reproduce scaling exponent greater than 2. The scaling exponents greater than 2 are associated with the velocity shear of the mean flow.