• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.229-236
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• 2011

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.48-55
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• 2003

Hidden Markov Model(HMM) has a doubly embedded stochastic process with an underlying stochastic process that can be observed through another set of stochastic processes. This structure of HMM is useful for modeling vector sequence that doesn't look like a stochastic process but has a hidden stochastic process. So, HMM approach has become popular in various areas in last decade. The increasing popularity of HMM is based on two facts : rich mathematical structure and proven accuracy on critical application. In this paper, we applied continuous HMM (CHMM) approach with AR coefficient to detect and predict the chatter of lathe bite and to diagnose the wear of oil Journal bearing using rotor shaft displacement. Our examples show that CHMM approach is very efficient method for machine health monitoring and prediction.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.183-193
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• 2019

Process mining is an analytical technique aimed at obtaining useful information about a process by extracting a process model from events log. However, most existing process models are deterministic because they do not include stochastic elements such as the occurrence probabilities or execution times of activities. Therefore, available information is limited, resulting in the limitations on analyzing and understanding the process. Furthermore, it is also important to develop an efficient methodology to discover the process model. Although genetic process mining algorithm is one of the methods that can handle data with noises, it has a limitation of large computation time when it is applied to data with large capacity. To resolve these issues, in this paper, we define a stochastic process tree and propose a tabu search-genetic process mining (TS-GPM) algorithm for a stochastic process tree. Specifically, we define a two-dimensional array as a chromosome to represent a stochastic process tree, fitness function, a procedure for generating stochastic process tree and a model trace as a string of activities generated from the process tree. Furthermore, by storing and comparing model traces with low fitness values in the tabu list, we can prevent duplicated searches for process trees with low fitness value being performed. In order to verify the performance of the proposed algorithm, we performed a numerical experiment by using two kinds of event log data used in the previous research. The results showed that the suggested TS-GPM algorithm outperformed the GPM algorithm in terms of fitness and computation time.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.6
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• pp.3273-3308
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• 2017

Building appropriate trust evaluation models is an important research issue for security guarantee in social networks. Most of the existing works usually consider the trust values at the current time slot, and model trust as the stochastic variable. However, in fact, trust evolves over time, and trust is a stochastic process. In this paper, we propose a novel time-variant stochastic trust evaluation (TSTE) model, which models trust over time and captures trust evolution by a stochastic process. Based on the proposed model, we derive the time-variant bound of untrustworthy probability, which provides stochastic trust guarantee. On one hand, the time-variant trust level of each node can be measured by our model. Meanwhile, by tolerating nodes with relatively poor performance, our model can effectively improve the node resource utilization rate. Numerical simulations are conducted to verify the accuracy and consistency of the analytical bounds on distinguishing misbehaved nodes from normal ones. Moreover, simulation results on social network dataset show the tradeoff between trust level and resource utilization rate, and verify that the successful transmission rate can be improved by our model.

• Korean Journal of Computational Design and Engineering
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• v.17 no.2
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• pp.111-122
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• 2012

Capacity planning plays an important role not only for master production plan but also for facility or layout design in shipbuilding. Product work breakdown structure, attributes of production resources, and production method or process data are associated in order to make the discrete event simulation model of shipyard layout plan. The production amount of each process and the process time is assumed to be stochastic. Based on the stochastic discrete event simulation model, the production capacity of each facility in shipyard is estimated. The stochastic model of product arrival time, process time and transferring time is introduced for each process. Also, the production capacity is estimated for the assumed master production schedule.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.697-704
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents the stochastic model of a nonlinear dynamic system with uncertain parameters under nonstationary stochastic inputs. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method and the second moment equation is numerically evaluated by stochastic process closure method, 4th cumulant neglect closure method and Runge-Kutta method. But the first and the second moment equations are coupled each other, so this equations are approximately evaluated by a iterative method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.397-407
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• 2006

A new stochastic process is introduced for describing a mechanism of viruses. The process generalizes the $Bartoszy\'{n}ski's$ process ($Bartoszy\'{n}ski$, 1975a, 1975b, 1976) by allowing the stochastic perturbation between consecutive jumps to take into account the persistent infection (the infection without breaking infected cells). It is shown that the new process can be obtained by a weak limit of a sequence of Markov branching processes. Along with the construction of the new process, we study how the stochastic perturbation influences the risk of a symptom in an infected host. For this purpose, the quantal response model and the threshold model are investigated and compared through their induced survival functions.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.491-502
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• 2015

A martingale is a mathematical model for a fair wager and the modern theory of martingales plays a very important and useful role in the study of the stochastic fields. This paper is devoted to investigate a martingale and a non-martingale on the several stochastic integral or differential equations. Specially, we show that whether the stochastic integral equation involving a standard Wiener process with the associated filtration is or not a martingale.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.291-297
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• 2001

For a stochastic regression model in which the errors are assumed to form a stationary linear process, we show that the difference between the empirical distribution functions of the errors and the estimates of those errors converges uniformly in probability to zero at the rate of $o_{p}$ ( $n^{-}$$\frac{1}{2}$) as the sample size n increases.

• International Journal of Reliability and Applications
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• v.4 no.1
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.