• Title/Summary/Keyword: stochastic processes

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BACKWARD SELF-SIMILAR STOCHASTIC PROCESSES IN STOCHASTIC DIFFERENTIAL EQUATIONS

  • Oh, Jae-Pill
    • Korean Journal of Mathematics
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    • v.6 no.2
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    • pp.259-279
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    • 1998
  • For the forward-backward semimartingale, we can define the backward semimartingale flow which is generated by the backward canonical stochastic differential equation. Therefore, we define the backward self-similar stochastic processes, and we study the backward self-similar stochastic flows through the canonical stochastic differential equations.

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Simulation of non-Gaussian stochastic processes by amplitude modulation and phase reconstruction

  • Jiang, Yu;Tao, Junyong;Wang, Dezhi
    • Wind and Structures
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    • v.18 no.6
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    • pp.693-715
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    • 2014
  • Stochastic processes are used to represent phenomena in many diverse fields. Numerical simulation method is widely applied for the solution to stochastic problems of complex structures when alternative analytical methods are not applicable. In some practical applications the stochastic processes show non-Gaussian properties. When the stochastic processes deviate significantly from Gaussian, techniques for their accurate simulation must be available. The various existing simulation methods of non-Gaussian stochastic processes generally can only simulate super-Gaussian stochastic processes with the high-peak characteristics. And these methodologies are usually complicated and time consuming, not sufficiently intuitive. By revealing the inherent coupling effect of the phase and amplitude part of discrete Fourier representation of random time series on the non-Gaussian features (such as skewness and kurtosis) through theoretical analysis and simulation experiments, this paper presents a novel approach for the simulation of non-Gaussian stochastic processes with the prescribed amplitude probability density function (PDF) and power spectral density (PSD) by amplitude modulation and phase reconstruction. As compared to previous spectral representation method using phase modulation to obtain a non-Gaussian amplitude distribution, this non-Gaussian phase reconstruction strategy is more straightforward and efficient, capable of simulating both super-Gaussian and sub-Gaussian stochastic processes. Another attractive feature of the method is that the whole process can be implemented efficiently using the Fast Fourier Transform. Cases studies demonstrate the efficiency and accuracy of the proposed algorithm.

Stochastic convexity in markov additive processes (마코프 누적 프로세스에서의 확률적 콘벡스성)

  • 윤복식
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 1991.10a
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    • pp.147-159
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    • 1991
  • Stochastic convexity(concvity) of a stochastic process is a very useful concept for various stochastic optimization problems. In this study we first establish stochastic convexity of a certain class of Markov additive processes through the probabilistic construction based on the sample path approach. A Markov additive process is obtained by integrating a functional of the underlying Markov process with respect to time, and its stochastic convexity can be utilized to provide efficient methods for optimal design or for optimal operation schedule of a wide range of stochastic systems. We also clarify the conditions for stochatic monotonicity of the Markov process, which is required for stochatic convexity of the Markov additive process. This result shows that stochastic convexity can be used for the analysis of probabilistic models based on birth and death processes, which have very wide application area. Finally we demonstrate the validity and usefulness of the theoretical results by developing efficient methods for the optimal replacement scheduling based on the stochastic convexity property.

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Stochastic convexity in Markov additive processes and its applications (마코프 누적 프로세스에서의 확률적 콘벡스성과 그 응용)

  • 윤복식
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.1
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    • pp.76-88
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    • 1991
  • Stochastic convexity (concavity) of a stochastic process is a very useful concept for various stochastic optimization problems. In this study we first establish stochastic convexity of a certain class of Markov additive processes through probabilistic construction based on the sample path approach. A Markov additive process is abtained by integrating a functional of the underlying Markov process with respect to time, and its stochastic convexity can be utilized to provide efficient methods for optimal design or optimal operation schedule wide range of stochastic systems. We also clarify the conditions for stochastic monotonicity of the Markov process. From the result it is shown that stachstic convexity can be used for the analysis of probabilitic models based on birth and death processes, which have very wide applications area. Finally we demonstrate the validity and usefulness of the theoretical results by developing efficient methods for the optimal replacement scheduling based on the stochastic convexity property.

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Bounding Methods for Markov Processes Based on Stochastic Monotonicity and Convexity (확률적 단조성과 콘벡스성을 이용한 마코프 프로세스에서의 범위한정 기법)

  • Yoon, Bok-Sik
    • Journal of Korean Institute of Industrial Engineers
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    • v.17 no.1
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    • pp.117-126
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    • 1991
  • When {X(t), t ${\geq}$ 0} is a Markov process representing time-varying system states, we develop efficient bounding methods for some time-dependent performance measures. We use the discretization technique for stochastically monotone Markov processes and a combination of discretization and uniformization for Markov processes with the stochastic convexity(concavity) property. Sufficient conditions for stochastic monotonocity and stochastic convexity of a Markov process are also mentioned. A simple example is given to demonstrate the validity of the bounding methods.

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A WEAK ORDERING OF POSITIVE DEPENDENCE STRUCTURE OF STOCHASTIC PROCESSES

  • Ryu, Dae-Hee;Seok, Eun-Yang;Choi, In-Bong
    • Journal of applied mathematics & informatics
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    • v.5 no.2
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    • pp.553-564
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    • 1998
  • In this paper we introduce a new concept of more weakly quadrant dependence of hitting times of stochastic processes. This concept is weaker than the more positively quadrant dependence of hitting times of stochastic processes. This concept is weaker than the more positively quadrant dependence and it is closed under some statistical operations of weakly positive quadrant dependence(WPQD) ordering.

Stochastic optimal control of coupled structures

  • Ying, Z.G.;Ni, Y.Q.;Ko, J.M.
    • Structural Engineering and Mechanics
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    • v.15 no.6
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    • pp.669-683
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    • 2003
  • The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

Derivation of response spectrum compatible non-stationary stochastic processes relying on Monte Carlo-based peak factor estimation

  • Giaralis, Agathoklis;Spanos, Pol D.
    • Earthquakes and Structures
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    • v.3 no.5
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    • pp.719-747
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    • 2012
  • In this paper a novel approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. The appealing feature of the approach is that it is non-iterative and "one-step". This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various "two-step" approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.

Derivation of response spectrum compatible non-stationary stochastic processes relying on Monte Carlo-based peak factor estimation

  • Giaralis, Agathoklis;Spanos, Pol D.
    • Earthquakes and Structures
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    • v.3 no.3_4
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    • pp.581-609
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    • 2012
  • In this paper a novel non-iterative approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.