• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.959-973
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• 2005

In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.259-279
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• 1998

For the forward-backward semimartingale, we can define the backward semimartingale flow which is generated by the backward canonical stochastic differential equation. Therefore, we define the backward self-similar stochastic processes, and we study the backward self-similar stochastic flows through the canonical stochastic differential equations.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.133-146
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• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• The KIPS Transactions:PartC
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• v.10C no.7
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• pp.899-914
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• 2003

It is generally accepted that self-similar (or fractal) processes may provide better models for 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. Three generators of pseudo-random self-similar sequences, based on the FFT〔20〕, RMD〔12〕 and SRA methods〔5, 10〕, are compared and analysed in this paper. Properties of these generators were experimentally studied in the sense of their statistical accuracy and times required to produce sequences of a given (long) length. While all three generators show similar levels of accuracy of the output data (in the sense of relative accuracy of the Horst parameter), the RMD- and SRA-based generators appear to be much faster than the generator based on FFT. Our results also show that a robust method for comparative studies of self-similarity in pseudo-random sequences is needed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.11
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• pp.1946-1958
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• 2011

Wireless Sensor Network (WSN) is made up of a number of sensor nodes and base stations. Traffic flow in WSN appears self-similar due to its data delivery process, and this impacts queue length greatly and makes queuing delay worse. Active queue management can be designed to improve QoS performance for WSN. In this paper, we propose self-similar traffic rate estimating algorithm named Power-Law Moving Averaging (PLMA) to regulate packet marking probability. This algorithm improves the availability of the rate estimation algorithm under the self-similar traffic condition. Then, we propose an adaptive Proportional Integral algorithm (SSPI) based on the estimation of the Self-Similar traffic rate by PLMA. Simulation results show that SSPI can achieve lower queue length jitter and smaller setting time than PI.

• 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).

• 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/$\alpha$.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.585-594
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• 2006

We consider a stochastic integral process represented by multiple Ito-Wiener integrals. We derive gaussian chaos which has some shift continuous function. We get continuity property of self-similar process represented by multiple integrals and finally we show that $Y_{H_t}$ (t) is continuous in t with probability one for Holder function $H_t$ of exponent $\beta$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.4B
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• pp.162-169
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• 2005

Network traffic measurements show that the data traffic on packet switched networks has the self-similar features which is different from the traditional traffic models such as Poisson distribution or Markovian process model. Most of the call admission control researches have been done on the performance analysis of a single network switch. It is necessary to consider the performance analysis of the proposed admission control scheme under interconnected switch environment because the data traffic transmits through switches in networks. From the simulation results, it is shown that the call admission control scheme may not operate properly on the interconnected switch even though the scheme works well on a single switch. In this parer, we analyze the cell loss probability, utilization and self-similarity of output ports of the interconnected networks switch by using shared buffer memory management schemes and propose the new call admission control scheme considering the interconnected network switches under self-similar traffic environments.