• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.45-57
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• 2011

We study the stochastic integral of an operator valued process against with a Banach space valued regular process. We establish the existence and uniqueness of solution of the stochastic differential equation for a Banach space valued regular process under the certain conditions. As an application of it, we study a noncommutative stochastic differential equation.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.167-178
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• 2016

In this paper, we study the stochastic integral of processes taking values of generalized operators based on a triple E ⊂ H ⊂ E^∗, where H is a Hilbert space, E is a countable Hilbert space and E^∗ is the strong dual space of E. For our purpose, we study E-valued Wiener processes and then introduce the stochastic integral of L(E, F^∗)-valued process with respect to an E-valued Wiener process, where F^∗ is the strong dual space of another countable Hilbert space F.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.71-94
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• 2009

In this paper a procedure for Monte Carlo simulation of univariate stationary stochastic processes with the aid of neural networks is presented. Neural networks operate model-free and, thus, circumvent the need of specifying a priori statistical properties of the process, as needed traditionally. This is particularly advantageous when only limited data are available. A neural network can capture the "pattern" of a short observed time series. Afterwards, it can directly generate stochastic process realizations which capture the properties of the underlying data. In the present study a simple feed-forward network with focused time-memory is utilized. The proposed procedure is demonstrated by examples of Monte Carlo simulation, by synthesis of future values of an initially short single process record.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.311-319
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• 2001

We show that it is possible to associate diffusion processes to second order perturbations of the Ornstein-Uhlenbeck operator L on the Wiener space of the form L = L + 1/2∑L$^2$(sub)ξ(sub)$\kappa$ where the ξ(sub)$\kappa$ are "tangent processes" (i.e., semimartingales with antisymmetric diffusion coefficients).

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.543-550
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• 2017

In this paper, we introduced a new asymptotic pairwise negatively dependent(APND) structure of stochastic processes. We are also important to know the degree of APND-ness and to compare pairs of stochastic vectors as to their APND-ness. So, we introduced a definitions and some basic properties of APND ordering. Some preservation results of APND ordering are derived. Finally, we shown some examples and applications.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.103-110
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• 1992

In this paper, T. Kawata's result[2] is generalized, by means of Beurling's norm, in the case of periodic stochastic processes of the second order which belong to Lipschitz class.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.91-112
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• 2009

The bullwhip effect means the phenomenon of increasing demand variation as moving UP to the upstream in the supply chain. Therefore, it is recognized that the bullwhip effect is problematic for effective supply chain operations. In this paper, we exactly quantifies the bullwhip effect for the case of stochastic lead time and seasonal demand in two-echelon supply chain where retailer employs a base-stock policy considering SARMA demand processes and stochastic lead time. We also investigate the behavior of the proposed measurement for the bullwhip effect with autoregressive and moving average coefficient, stochastic lead time, and seasonal factor.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.161-169
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• 2014

We in this paper obtained the theoretical results for multivariate stochastic processes which help us to extended negatively orthant dependent(ENOD) structures among hitting times of the processes. In addition, some applications are given to illustrate these concepts.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.855-867
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• 2005

Shattering or disintegration of mass is a well known phenomenon in fragmentation processes first introduced by Kol­mogorov and Filippop and extensively studied by many physicists. Though the mass is conserved in each break-up, the total mass decreases in finite time. We investigate this phenomenon in the n particle system. In this system, shattering can be interpreted such that, in uniformly bounded time on n, order n of mass is located in order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze the phenomenon. For the newly defined stochastic shattering based on the above ideas, we derive far sharper conditions of fragmentation kernels which guarantee the occurrence of such a phenomenon than our previous work [9].