• Journal of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.819-833
• /
• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.7 no.8
• /
• pp.1674-1683
• /
• 2003

The performance of a packet data multiplexer with stop­and­wait ARQ protocols under Markovian interruption is considered in this work It is assumed that the input process, into the system is Poisson process, and that the output channel is divided into a series of time slots and a data packet can be transmitted in a slot time. In this system the round­trip propagation delay is defined to be the frame time. It is modeled that the output channel can be blocked by some Markevian interruption, whose state change between the blocking and non­-blocking states is given by Markov process. The overall system has been analyzed by constructing a relationship, taking the Markovian interruption into account, about the buffer behavior between the successive frames of slots. The validity of this analytical results has been verified by computer simulation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.12a
• /
• pp.153-156
• /
• 2001

This paper discusses a stochastic stabilization of Takagi-Sugeno (75) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time 75 fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretized 75 fuzzy system is represented by a discrete-time 75 fuzzy system with jumping parameters. The stochastic stabilizibility of the jump 75 fuzzy system is derived and formulated in terms of linear matrix inequalities (LMls).

• Proceedings of the KIEE Conference
• /
• 2008.10b
• /
• pp.235-236
• /
• 2008

This paper is concerned with the stabilization problem of Markovian jump nonlinear systems with time-delay via Takagi-Sugeno (T-S) fuzzy control approach. The T-S fuzzy models are employed to represent nonlinear systems with Markovian jump parameters and time-delay. The purpose of this paper is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. Based on a stochstic Lyapunov function, stabilization sufficient conditions using a mode-independent fuzzy controller are derived for the Markovian jump fuzzy system in terms of Linear Matrix Inequalities (LMIs). Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.387-397
• /
• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.6
• /
• pp.712-717
• /
• 2007

This paper is concerned with the problem of state feedback control of continuous-time nonlinear Markovian jump systems, which are represented by Takagi-Sugeno fuzzy models. A new method for designing state feedback stabilizing controllers is presented in terms of solvability of a set of linear matrix inequalities (LMIs), and it is shown that the new design method provides better or at least the same results of the existing method in the literature. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

• The Journal of the Acoustical Society of Korea
• /
• v.16 no.3E
• /
• pp.32-36
• /
• 1997

This study models mobile communication channels as a discrete finite Markovian process, and Markovian jump linear system having parallel Kalman filter type is applied. What is newly proposed in this paper is an equation for obtaining the transition matrix according to sampling time by using a weighted Gaussian sum approximation and its simple calculation process. Experiments show that the proposed method has superior performance and reuires computation compared to the existing MJLS using the ransition matrix given by a statistical method or from priori information.

• Communications of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.99-109
• /
• 2009

The aim of this paper is to find the set of the fixed elements and the set of elements for which equality holds in Schwarz inequality for the KMS-symmetric Markovian semigroup $\{S_t\}_{t{\geq}0}$ given in [10]. As an application, we study some properties such as the ergodicity and the asymptotic behavior of the semigroup.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.11 no.17
• /
• pp.81-85
• /
• 1988

This paper presents a model that considers combinations of rework, repair, replacement and scrapping. Policy-Iteration method of inspection is proposed for a serial manufacturing system whose repair cost, scrap cost and inspection cost. when it fails, can be formulated by Markovian approach. Policy-Iteration stops when new inspection policy is the same as previous inspection policy. A numerial example is presented.

• Journal of Korean Institute of Industrial Engineers
• /
• v.8 no.2
• /
• pp.15-21
• /
• 1982

This paper offers an alternative to the common probability generating function approach to the solution of steady state equations when a Markovian queue has a multivariate state space. Identifying states and substates and grouping them into vectors appropriately, we formulate a two - dimensional Markovian queue as a Markov chain. Solving the resulting matrix equations the transition point steady state probabilities (SSPs) are obtained. These are then converted into arbitrary time SSPs. The procedure uses only probabilistic arguments and thus avoids a large and cumbersome state space which often poses difficulties in the solution of steady state equations. For the purpose of numerical illustration of the approach we solve a Markovian queue with one server and two classes of customers.