• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.583-611
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• 1998

We consider a general class of real-valued Levy processes {X(t), $t\geq0$}, and obtain suitable large deviation results for the empiricals L(t, A) defined by $t^{-1}{\int^t}_01_A$(X(s)ds for t > 0 and a Borel subset A of R. These results are used to obtain the asymptotic behavior of P{Z(t) < a}, where Z(t) = $sup_{u\leqt}\midx(u)\mid$ as $t\longrightarrow\infty$, in terms of the rate function in the large deviation principle. A subclass of these processes is the Feller class: there exist nonrandom functions b(t) and a(t) > 0 such that {(X(t) - b(t))/a(t) : t > 0} is stochastically compact, i.e., each sequence has a weakly convergent subsequence with a nondegenerate limit. The stable processes are in this class, but it is much larger. We consider processes in this class for which b(t) may be taken to be zero. For any t > 0, we consider the renormalized process ${X(u\psi(t))/a(\psi(t)),u\geq0}$, where $\psi$(t) = $t(log log t)^{-1}$, and obtain large deviation probability estimates for $L_{t}(A)$ := $(log log t)^{-1}$${\int_{0}}^{loglogt}1_A$$(X(u\psi(t))/a(\psi(t)))dv$. It turns out that the upper and lower bounds are sharp and depend on the entire compact set of limit laws of {X(t)/a(t)}. The results extend to random walks in the Feller class as well. Earlier results of this nature were obtained by Donsker and Varadhan for symmetric stable processes and by Jain for random walks in the domain of attraction of a stable law.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.1-12
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• 2017

Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.801-811
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• 2008

Modeling financial phenomena with diffusion processes is a commonly used methodology in the area of modern finance. Recently, various types of diffusion models have been suggested to explain the specific financial processes, and their related inference methodology have been also developed. In particular, likelihood methods for the efficient and accurate inference have been explored in various ways. In this paper, we review the mathematical properties of an approximated likelihood method, which is obtained by linearizing the drift coefficient of a diffusion process.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.357-357
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• 2000

In this study, we consider a multi-input multi-output styrene polymerization reactor system for which the monomer conversion and the weight average molecular weight are controlled by manipulating the jacket inlet temperature and the feed flow rate. The reactor system is identified by using a linear subspace identification method and then the output feedback model predictive controller is constructed on the basis of the identified model. Here we use the Best Linear Unbiased Estimation (BLUE) filter as a stochastic estimator instead of the Kalman filter. The BLUE filter observes the state successfully without any a priori information of initial states. In contrast to the Kalman filter, the BLUE filter eliminates the offset by observing the state of the augmented system regardless of a priori information of the initial state for an integral white noise augmented system. A BLUE filter has a finite impulse response (FIR) structure which utilizes finite measurements and inputs on the most recent time interval [i-N, i] in order to avoid long processing times.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.2
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• pp.1148-1161
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• 2017

The success of a business process management system stands or falls on the quality of the business processes. Many experiments therefore have been devoting considerable attention to the modeling and analysis of business processes in process-centered organizations. One of those experiments is to apply the probabilistic theories to the analytical evaluations of business process models in order to improve their qualities. In this paper, we excogitate a conceptual way of applying a probability theory of proportions into modeling business processes. There are three types of routing patterns such as sequential, disjunctive, conjunctive and iterative routing patterns in modeling business processes, into which the proportion theory is applicable. This paper focuses on applying the proportion theory to the disjunctive routing patterns, in particular, and formally named proportional information control net that is the formal representation of a corresponding business process model. In this paper, we propose a conceptual approach to discover a proportional information control net from the enactment event histories of the corresponding business process, and describe the details of a series of procedural frameworks and operational mechanisms formally and graphically supporting the proposed approach. We strongly believe that the conceptual approach with the proportional information control net ought to be very useful to improve the quality of business processes by adapting to the reengineering and redesigning the corresponding business processes.

• Journal of Advanced Navigation Technology
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• v.19 no.6
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• pp.636-642
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• 2015

This paper presents an application of heuristic harmony search (HS) optimization algorithm for the identification of linear continuous time-delay system from step response. Identification model is first-order plus dead time (FOPDT), which describes a linear monotonic process quite well in most chemical processes and HAVC process and is often sufficient for PID controller tuning. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. The effectiveness of the identification method has been demonstrated through a number of simulation examples.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.277-288
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• 2014

This article reviews various state estimation methods for nonlinear systems, particularly with a perspective of a process control engineer. Nonlinear state estimation methods can be classified into the following two categories: stochastic approaches and deterministic approaches. The current review compares the Bayesian approach, which is mainly a stochastic approach, and the MHE (Moving Horizon Estimation) approach, which is mainly a deterministic approach. Though both methods are reviewed, emphasis is given to the latter as it is particularly well-suited to highly nonlinear systems with slow sampling rates, which are common in chemical process applications. Recent developments in underlying theories and supporting numerical algorithms for MHE are reviewed. Thanks to these developments, applications to large-scale and complex chemical processes are beginning to show up but they are still limited at this point owing to the high numerical complexity of the method.

• Journal of Communications and Networks
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• v.18 no.6
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• pp.926-937
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• 2016

In this paper, we study the feasibility of receiver diversity for application to downlink cellular networks, where low-energy devices are equipped with information decoding and energy harvesting receivers for simultaneous wireless information and power transfer. We compare several options that are based on selection combining and maximum ratio combining, which provide different implementation complexities. By capitalizing on the Frechet inequality, we shed light on the advantages and limitations of each scheme as a function of the transmission rate and harvested power that need to be fulfilled at the low-energy devices. Our analysis shows that no scheme outperforms the others for every system setup. It suggests, on the other hand, that the low-energy devices need to operate in an adaptive fashion, by choosing the receiver diversity scheme as a function of the imposed requirements. With the aid of stochastic geometry, we introduce mathematical frameworks for system-level analysis. We show that they constitute an important tool for system-level optimization and, in particular, for identifying the diversity scheme that optimizes wireless information and power transmission as a function of a sensible set of parameters. Monte Carlo simulations are used to validate our findings and to illustrate the trade-off that emerge in cellular networks with simultaneous wireless information and power transfer.

• Computers and Concrete
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• v.29 no.1
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• pp.1-14
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• 2022

Several aspects influence corrosive processes in reinforced concrete (RC) structures such as environmental conditions, structural geometry and mechanical properties. Since these aspects present large randomnesses, probabilistic models allow a more accurate description of the corrosive phenomena. Besides, the definition of limit states in the reliability assessment requires a proper mechanical model. In this context, this study proposes a straightforward methodology for the mechanical-probabilistic modelling of RC structures subjected to reinforcements' corrosion. An improved damage approach is proposed to define the limit states for the probabilistic modelling, considering three main degradation phenomena: concrete cracking, rebar yielding and rebar corrosion caused either by chloride or carbonation mechanisms. The stochastic analysis is evaluated by the Monte Carlo simulation method due to the computational efficiency of the Lumped Damage Model for Corrosion (LDMC). The proposed mechanical-probabilistic methodology is implemented in a computational framework and applied to the analysis of a simply supported RC beam and a 2D RC frame. Curves illustrate the probability of failure evolution over a service life of 50 years. Moreover, the proposed model allows drawing the probability of failure map and then identifying the critical failure path for progressive collapse analysis. Collapse path changes caused by the corrosion phenomena are observed.

• Journal of the Korean Operations Research and Management Science Society
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• v.40 no.1
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• pp.117-128
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• 2015

An organization must restructure itself once it makes outsourcing decisions. Outsourcing is a strategy that a company adopts to direct internal efforts into strengthening its core business processes while contracting other companies for strategically less critical tasks thereby improving organizational production efficiency, and the strategy inevitably involves organizational restructuring. While public service organizations have increasingly embraced outsourcing as well, only a handful of studies analyze the change in efficiency from organizational restructuring. Therefore, this study uses Stochastic Frontier Analysis (SFA) to test whether efficiency improved in Korea Expressway Corporation's restructured branch offices. Korea Expressway Corporation evaluated and grouped its branches based on road extensions management, traffic volume, the number of snow days, road deterioration, and the number of junctions to differentially allocate its personnel and budget. The extent of efficiency improvement in each group was compared, and results show that inefficiency did not exist in any of the groups. The efficiency index among the three group categories was similar across the board; 9 offices in the A-group with its expanded personnel and budget had an efficiency index of 0.954, 12 offices in the B-group with unchanged personnel and budget conditions had an index of 0.950, and 12 offices in the C-group with reduced personnel and budget had an index of 0.937. SFA facilitates efficiency analyses because it does not require pre-restructuring data. This study is easy to apply in practice and empirically tests efficiency improvement in organizational restructuring based on data collected from all the branch offices in Korea Expressway Corporation.