• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.9
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• pp.753-760
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• 1989

A method is suggested to design a stochastic observer which can be used as a state estimator for the optimal control of a one link flexible manipulator. This stochastic observer is derived from unifying the two concepts of reduced-state deterministic observer theory and optimal Kalman filtering theory. In estimating state variables for the optimal control, instead of using the two different state estimators for the deterministic system with noise free measurements and stochastic system with noise measurements, only one stochastic observer is designed which is to be used in both systems commonly. Through the simulation, it has been shown that the flexible system with the stochastic observer is similar in characteristics to the flexible system assuming that all states can be measured.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.491-502
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• 2015

A martingale is a mathematical model for a fair wager and the modern theory of martingales plays a very important and useful role in the study of the stochastic fields. This paper is devoted to investigate a martingale and a non-martingale on the several stochastic integral or differential equations. Specially, we show that whether the stochastic integral equation involving a standard Wiener process with the associated filtration is or not a martingale.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.4
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• pp.348-353
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• 2013

Recently, control theory including stochastic optimal control and various machine-learning-based artificial intelligence methods have become major tools in the field of financial engineering. In this paper, we briefly review some recent papers utilizing stochastic optimal control theory in the fields of the pair trading for mean-reverting markets and the trend-following strategy, and consider a couple of strategies utilizing both stochastic optimal control theory and machine learning methods to acquire more flexible and accessible tools. Illustrative simulations show that the considered strategies can yield encouraging results when applied to a set of real financial market data.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.335-354
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• 2007

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (${\hat}It{o}$ type) stochastic integrals with respect to the generalized Wiener process and prove the ${\hat}It{o}$ formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.753-759
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• 2002

In this paper, sufficient conditions for the controllability of stochastic integrodifferential systems in Banach spaces are established. The results are obtained by using a fixed point theorem. An example is provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Geomechanics and Engineering
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• v.14 no.6
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• pp.571-580
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• 2018

The failure mechanism of tunnel roof is investigated with upper bound theorem of limit analysis. The stochastic settlement and nonlinear failure criterion are considered in the present analysis. For the collapse of tunnel roof, the surface settlement is estimated by the simplified stochastic medium theory. The failure curve expressions of collapse blocks in homogeneous and in layered soils are derived, and the effects of material parameters on the potential range of failure mechanisms are discussed. The results show that the material parameters of initial cohesion, nonlinear coefficient and unit weight have significant influences on the potential range of collapse block in homogeneous media. The proportion of collapse block increases as the initial cohesion increases, while decreases as the nonlinear coefficient and the unit weight increase. The ground surface settlement increases with the tunnel radius increasing, while the possible collapse proportion decreases with increase of the tunnel radius. In layered stratum, the study is investigated to analyze the effects of material parameters of different layered media on the proportion of possible collapse block.

• Journal of Ubiquitous Convergence Technology
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• v.2 no.2
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• pp.105-110
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• 2008

The definition of the program control is introduced on the theory of the basis of the first integrals SDE system. That definition allows constructing the program control gives opportunity to stochastic system to remain on the given dynamic variety. The program control is considered in terms of dynamically invariant for stochastic process.