• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.917-933
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• 2017

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.699-701
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• 1997

The simulated annealing(SA) algorithm is a stochastic strategy for search of the ground state and a powerful tool for optimization, based on the annealing process used for the crystallization in physical systems. It's main disadvantage is the long convergence time. Therefore, this paper proposes a stochastic algorithm combined with conventional deterministic optimization method to reduce the computation time, which is called SDS(Stochastic-Deterministic-Stochastic) method.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• East Asian Economic Review
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• v.25 no.4
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• pp.403-424
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• 2021

AdaBoost tweaks the sample weight for each training set used in the iterative process, however, it is demonstrated that it provides more correlated errors as the boosting iteration proceeds if models' accuracy is high enough. Therefore, in this study, we propose a novel way to improve the performance of the existing AdaBoost algorithm by employing heterogeneous models and a stochastic twist. By employing the heterogeneous ensemble, it ensures different models that have a different initial assumption about the data are used to improve on diversity. Also, by using a stochastic algorithm with a decaying convergence rate, the model is designed to balance out the trade-off between model prediction performance and model convergence. The result showed that the stochastic algorithm with decaying convergence rate's did have a improving effect and outperformed other existing boosting techniques.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Journal of Communications and Networks
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• v.18 no.3
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• pp.411-419
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• 2016

This article investigates the problem of distributed channel selection in opportunistic spectrum access networks from a perspective of interference minimization. The traditional physical (PHY)-layer interference model is for information theoretic analysis. When practical multiple access mechanisms are considered, the recently developed binary medium access control (MAC)-layer interference model in the previous work is more useful, in which the experienced interference of a user is defined as the number of competing users. However, the binary model is not accurate in mathematics analysis with poor achievable performance. Therefore, we propose a real-valued one called stochastic MAC-layer interference model, where the utility of a player is defined as a function of the aggregate weight of the stochastic interference of competing neighbors. Then, the distributed channel selection problem in the stochastic MAC-layer interference model is formulated as a weighted stochastic MAC-layer interference minimization game and we proved that the game is an exact potential game which exists one pure strategy Nash equilibrium point at least. By using the proposed stochastic learning-automata based uncoupled algorithm with heterogeneous learning parameter (SLA-H), we can achieve suboptimal convergence averagely and this result can be verified in the simulation. Moreover, the simulated results also prove that the proposed stochastic model can achieve higher throughput performance and faster convergence behavior than the binary one.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.457-467
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• 2013

There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1303-1315
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• 2018

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method [11] to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in [24]. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.559-570
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• 2008

This paper proposes an improved particle swarm optimization named PSO with Controllable Random Exploration Velocity (PSO-CREV) behaving an additional exploration behavior. Different from other improvements on PSO, the updating principle of PSO-CREV is constructed in terms of stochastic approximation diagram. Hence a stochastic velocity independent on cognitive and social components of PSO can be added to the updating principle, so that particles have strong exploration ability than those of conventional PSO. The conditions and main behaviors of PSO-CREV are described. Two properties in terms of "divergence before convergence" and "controllable exploration behavior" are presented, which promote the performance of PSO-CREV. An experimental method based on a complex test function is proposed by which the proper parameters of PSO-CREV used in practice are figured out, which guarantees the high exploration ability, as well as the convergence rate is concerned. The benchmarks and applications on FCRNN training verify the improvements brought by PSO-CREV.