• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.311-330
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• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.299-315
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• 2022

This manuscript deals with the exact (complete) controllability of semilinear stochastic differential equations with infinite delay and Poisson jumps utilizing some basic and readily verified conditions. The results are obtained by using fixed-point approach and by using advance phase space definition for infinite delay part. We have used the axiomatic definition of the phase space in terms of stochastic process to consider the time delay of the system. An infinite delay along with the Poisson jump is the new investigation for the given stochastic system. An example is given to illustrate the effectiveness of the results.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.1
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• pp.20-24
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• 2008

A bid-based pool(BBP) model is representative of energy market structure in a number of restructured electricity markets. Supply function equilibrium(SFE) models of interaction better match what is explicitly required in the bid formats of typical BBP markets. Many of the results in the SFE literature involve restrictive parametrization of the bid cost functions. In the SFE models, two parameters, intercept and slope, are available for strategic bidding. This paper addresses the realistic competition format that players can choose both parameters arbitrarily. In a fixed demand function, equilibrium conditions for generation company's profit maximization have a degree of freedom, which induces multi-equilibrium. So it is hard to choose a convergent equilibrium. However, consideration of stochastic demand function makes the equilibrium conditions independent each other based on the amount of variance of stochastic demand function. This variance provides the bidding players with incentives to change the slope parameter from an equilibrium for a fixed demand function until the slope parameter equilibrium.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.427-435
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• 2007

The existence theorem and continuous dependence property in $"L^2"$ sense for solutions of backward stochastic differential equation (shortly BSDE) with Lipschitz coefficients were respectively established by Pardoux-Peng and Peng in [1,2], Mao and Cao generalized the Pardoux-Peng's existence and uniqueness theorem to BSDE with non-Lipschitz coefficients in [3,4]. The present paper generalizes the Peng's continuous dependence property in $"L^2"$ sense to BSDE with Mao and Cao's conditions. Furthermore, this paper investigates the continuous dependence property in "almost surely" sense for BSDE with Mao and Cao's conditions, based on the comparison with the classical mathematical expectation.

• Wind and Structures
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• v.22 no.5
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• pp.525-541
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• 2016

An offshore wind turbine supported by a spar buoy floating platform is the subject of this study on tower and rotor extreme loads. The platform, with a 120-meter draft and assumed to be sited in 320 meters of water, supports a 5 MW wind turbine. A baseline model for this turbine developed at the National Renewable Energy Laboratory (NREL) is employed in stochastic response simulations. The support platform, along with the mooring system consisting of three catenary lines, chosen for loads modeling, is based on the "Hywind" floating wind turbine concept. Our interest lies in gaining an understanding of the dynamic coupling between the support platform motion and the turbine loads. We first investigate short-term response statistics using stochastic simulation for a range of different environmental wind and wave conditions. From this study, we identify a few "controlling" environmental conditions for which long-term turbine load statistics and probability distributions are established.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Journal of the Korea Society for Simulation
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• v.22 no.4
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• pp.21-28
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• 2013

This paper describes the method to solve the optimization problems for stochastic simulation which is represented by military simulations. For this reason, the test fitness function reflecting the characteristics of military simulations, complex and stochastic results, is defined and PSO is used to solve the test fitness function. To control the known weak point of PSO for stochastic simulations, this paper proposes a technique which reevaluates the value of global optimum. By using the technique, the result shows notable improvements. From the simulation results, interactions among the calculation conditions which affect the accuracy and speed of optimization are analyzed. And the strategy for the optimization of stochastic simulations is proposed.

• Journal of Electrical Engineering and Technology
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• v.13 no.3
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• pp.1110-1122
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• 2018

This paper proposes an alternative method to evaluate the effect of wind power to the power system stability with small disturbance. Alternatively, available techniques for stability analysis of a power system based on deterministic methods are less accurate for high penetration of wind power. Numerical simulations of random behaviors are computationally expensive. A stochastic stability index (SSI) is proposed for the power system stability evaluation based on the theory of stochastic stability and energy function, specifically the stochastic derivative of the relative well-defined energy function and the critical energy. The SSI is implemented on the modified nine-bus system including wind turbines under different conditions. A doubly-fed induction generator (DFIG) wind turbine is characterized and modeled using measured wind data from several sites in Thailand. Each of the obtained wind power data is analyzed. The wind power effect is modeled considering the aggregated effect of wind turbines. With the proposed method, the system behavior is properly predicted and the stability is quantitatively evaluated with less computational effort compared with conventional numerical simulation methods.