• Magazine of the Korean Society of Agricultural Engineers
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• 제36권1호
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• pp.54-62
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• 1994

The expanding technique of the Stochastic Finite Element Method(SFEM) is proposed in this paper for adapting direct integration methods in stochastical dynamic analysis of structures. Grafting the direct integration methods and the SFEM together, one can deal with nonlinear structures and nonstationary process problems without any restriction. The stochastical central diffrence and stochastic Houbolt methods are introduced to show the expanding technique, and their adaptabilities are discussed. Results computed by the proposed method (the Stochastic Finite Element Method in Dynamics: SFEMD) for two degree-of-free- dom system are compared with those obtained by Monte Carlo Simulation.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.639-647
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• 2021

In this paper, we consider the integral of a stochastic process with respect of a sequence of square integrable semimartingales. By this integrals, we construct a reproducing kernel Hilbert space and study the correspondence between this space with the concepts of arbitrage and viability in mathematical finance.

• Structural Engineering and Mechanics
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• 제3권3호
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• pp.273-287
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• 1995

Stochastic response of systems to random excitation can be estimated by direct integration methods in the time domain such as the stochastic central difference method (SCDM). In this paper, the SCDM is applied to compute the variance and covariance in response of linear and nonlinear structures subjected to random excitation. The accuracy of the SCDM is assessed using two-DOF systems with both deterministic and random material properties excited by white noise. For the former case, closed-form solutions can be obtained. Numerical results also are presented for a simply supported geometrically nonlinear beam. The stiffness of this beam is modeled as a random field, and the beam is idealized by the stochastic finite element method. A perturbation technique is applied to formulate the equations of motion of the system, and the dynamic structural response statistics are obtained in a time domain analysis. The effect of variations in structural parameters and the numerical stability of the SCDM also are examined.

• Structural Engineering and Mechanics
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• 제63권6호
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• pp.789-797
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• 2017

Recently, some integrated structural identification/damage detection and reliability evaluation of structures with uncertainties have been proposed. However, these techniques are applicable for off-line synthesis of structural identification and reliability evaluation. In this paper, based on the recursive formulation of the extended Kalman filter, an on-line integration of structural identification/damage detection and reliability evaluation of stochastic building structures is investigated. Structural limit state is expanded by the Taylor series in terms of uncertain variables to obtain the probability density function (PDF). Both structural component reliability with only one limit state function and system reliability with multi-limit state functions are studied. Then, it is extended to adopt the recent extended Kalman filter with unknown input (EKF-UI) proposed by the authors for on-line integration of structural identification/damage detection and structural reliability evaluation of stochastic building structures subject to unknown excitations. Numerical examples are used to demonstrate the proposed method. The evaluated results of structural component reliability and structural system reliability are compared with those by the Monte Carlo simulation to validate the performances of the proposed method.

• Bulletin of the Korean Mathematical Society
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• 제56권5호
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• pp.1129-1141
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• 2019

We propose a stochastic delay financial model which describes influences driven by historical events. The underlying is modeled by stochastic delay differential equation (SDDE), and the delay effect is modeled by a stopping time in coefficient functions. While this model makes good economical sense, it is difficult to mathematically deal with this. Therefore, we circumvent this model with similar delay effects but mathematically more tractable, which is by the backward time integration. We derive the option pricing equation and provide the option price and the perfect hedging portfolio.

• Proceedings of the Korea Contents Association Conference
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• 한국콘텐츠학회 2010년도 춘계 종합학술대회 논문집
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• pp.390-392
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• 2010

Mobile grid system supports the integration mobile devices as grid resources. Availability of mobile resources changes dynamically in mobile grid system. Stochastic reward nets (SRN) is an extension of stochastic Petri nets and provides compact modeling facilities for system analysis. We build the SRN model to represent availability of mobile resources with disconnected operation service.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.101-115
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• 2005

We propose in this article a procedure for testing unit and fractional orders of integration, with the roots simultaneously occurring in the trend, the seasonal and the cyclical component of the time series. The tests have standard null and local limit distributions. However, finite sample critical values are computed, and several Monte Carlo experiments conducted across the paper show that the rejection frequencies against unit (and fractional) orders of integration are relatively high in all cases. The tests are applied to the UK consumption and income series, the results showing the importance of the roots corresponding to the trend and the seasonal components and, though the unit roots are found to be fairly suitable models, we show that fractional processes (including one for the cyclical component) may also be plausible alternatives in some cases.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• Transactions of the Korean Society of Machine Tool Engineers
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• 제13권2호
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• pp.81-87
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• 2004

This paper deals with a new approach to tolerance optimization problems. Optimal tolerance allotment problems can be formulated as stochastic optimization problems. Most schemes to solve the stochastic optimization problems have been found to exhibit difficulties in multivariate integration of the probability density function. As a typical example of stochastic optimization the optimal tolerance allotment problem has the same difficulties. In this stochastic model, manufacturing system is represented by Gauss-Markov stochastic process and the manufacturing unit availability is characterized for realistic optimization modeling. The new algorithm performed robustly for a large deviation approximation. A significant reduction in computation time was observed compared to the results obtained in previous studies.

• Journal of Ship and Ocean Technology
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• 제12권2호
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.