• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.49-52
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• 1999

A subspace-based identification method of the Wiener model, consisting of a state-space linear block and a polynomial static nonlinearity at the output, is used to retrieve from discrete sample data the accurate information about the nonlinear dynamics. Wiener model may be incorporated into model predictive control (MPC) schemes in a unique way which effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC. The control performance is evaluated with simulation studies where the original first-principles model for a continuous MMA polymerization reactor is used as the true process while the identified Wiener model is used for the control purpose. On the basis of the simulation results, it is demonstrated that, despite the existence of unmeasured disturbance, the controller performed quite satisfactorily for the control of polymer qualities with constraints.

• 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.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.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.23-34
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• 1992

This is an extension of results of Wiener's nonlinear noise theory from noises generated by the Wiener process to noises generated by processes with stationary Gaussian increments. In particular, using Nisio's Approach, we show that every measurable ergodic noise can be approximated in law by Gaussian process-presentable noise.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.501-506
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• 1998

A mathematical model is developed to describe the relationship between the manipulated variables (e.g. jacket inlet temperature and feed flow rate) and the important qualities (e.g conversion and weight average molecular weight (Mw)) in a continuous polymerization reactor. The subspace-based identification method for Wiener model is used to retrieve from the discrete sample data the accurate information about both the structure and initial parameter estimates for iterative parameter optimization methods. The comparison of the output of the identified Wiener model with the outputs of a non-linear plant model shows a fairly satisfactory degree of accordance.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.57-74
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• 1997

Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.813-822
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• 1996

Let ${W(t); 0 \leq t < \infty}$ be a standard Wiener process on a probability space $(\Omega, \Im , P)$.

• 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.

• Korean Chemical Engineering Research
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• v.61 no.1
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• pp.89-96
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• 2023

The Wiener-type nonlinear model where a static nonlinear block follows a dynamic linear block is widely used to describe the dynamics of chemical processes. A long process excitation step is typically needed to identify this Wiener-type nonlinear model with two blocks. In order to cope with this disadvantage, an identification method for the Wiener-type nonlinear model that uses only a single-step response is proposed here. The proposed method estimates the response of the dynamic linear sub-block from the initial part of the step response, and then the static nonlinear sub-block is identified. Because the only single-step response is used to identify the Wiener-type nonlinear model, there is great benefit in time and cost for obtaining process response. The performance of the proposed identification method with the single-step response is verified through a representative Wiener-type nonlinear process, a pH titration process, and a liquid level system.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.