共查询到20条相似文献,搜索用时 46 毫秒
1.
Yoshiyuki Suzuki 《Sadhana》1995,20(2-4):475-488
A method of stochastic optimal control of hysteretic structural systems under earthquake excitations is presented. Stochastic estimation and control problems are formulated in the form of Itô stochastic differential equations on the basis of the theory of continuous Markov processes. The conditional moment equations given observation data are derived for nonlinear filtering, and are closed by introducing appropriate analytical form of the conditional probability density functions of the state variables. Under the assumption that the admissible controls are expressed as functions of the conditional moment functions the Bellman equation is derived. If the spatial variables of the Bellman equation are defined by a part of the full set of conditional moment functions appearing in the closed moment equations, the resulting Bellman equation is coupled with conditional moment equations both for filtering and for prediction. The Gaussian and non-Gaussian stochastic linearization techniques combined with simple solution techniques to the Bellman equation are examined to solve the Bellman equation or extended Riccati equations without prediction procedures. 相似文献
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对Hilbert空间中具有Markovian参数的随机泛函微分时滞方程的指数稳定性进行了讨论。利用指数鞅公式,Lyapunov函数和一些不等式给出系统指数稳定的充分条件。这是对已有结果的完善和推广。通过一个例了对本文的结论进行了说明。 相似文献
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Xiaopeng Chen Anthony J. Roberts Jinqiao Duan 《Dynamical Systems: An International Journal》2019,34(2):334-355
Stochastic centre manifolds theory are crucial in modelling the dynamical behaviour of complex systems under stochastic influences. The existence of stochastic centre manifolds for infinite dimensional random dynamical systems is shown under the assumption of exponential trichotomy. The theory provides a support for the discretisations of nonlinear stochastic partial differential equations with space–time white noise. 相似文献
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Mark A. Lawrence 《International journal for numerical methods in engineering》1987,24(10):1849-1863
Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first- and second-moment properties of the solution to be calculated. An equivalent energy-based approach similar to the Rayleigh–Ritz method is developed, from which a stochastic finite element technique is derived. Several one- and two-dimensional example problems are solved and the results discussed. 相似文献
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A. Nouy A. Clément 《International journal for numerical methods in engineering》2010,83(10):1312-1344
An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a marriage between the eXtended Finite Element Method and spectral stochastic methods. In this article, we propose an extension of this method for the numerical simulation of random multi‐phased materials. The random geometry of material interfaces is described implicitly by using random level set functions. A fixed deterministic finite element mesh, which is not conforming to the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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P. Surya Mohan Prasanth B. Nair Andy J. Keane 《International journal for numerical methods in engineering》2011,85(7):874-895
We present stochastic projection schemes for approximating the solution of a class of deterministic linear elliptic partial differential equations defined on random domains. The key idea is to carry out spatial discretization using a combination of finite element methods and stochastic mesh representations. We prove a result to establish the conditions that the input uncertainty model must satisfy to ensure the validity of the stochastic mesh representation and hence the well posedness of the problem. Finite element spatial discretization of the governing equations using a stochastic mesh representation results in a linear random algebraic system of equations in a polynomial chaos basis whose coefficients of expansion can be non‐intrusively computed either at the element or the global level. The resulting randomly parametrized algebraic equations are solved using stochastic projection schemes to approximate the response statistics. The proposed approach is demonstrated for modeling diffusion in a square domain with a rough wall and heat transfer analysis of a three‐dimensional gas turbine blade model with uncertainty in the cooling core geometry. The numerical results are compared against Monte–Carlo simulations, and it is shown that the proposed approach provides high‐quality approximations for the first two statistical moments at modest computational effort. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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倒向随机微分方程理论搭起了随机与确定之间的桥梁,使人们可以用确定的策略方法去解决随机的不确定性问题,为金融产品的定价开辟了一条新的路径。因此,利用倒向随机微分方程理论研究了可分离债券的定价问题。首先,假设市场是无套利的,合理地建立了投资组合,通过自融资策略,用倒向随机微分方程理论得到了可分离债券价格所满足的倒向随机微分方程。接着,用非线性 Feynman-Kac 公式,得到了可分离债券价格所满足的偏微分方程,并证明了可分离债券在 0 时刻的价格等于到期现金流的条件期望,用鞅的方法得到了可分离债券价格的显示公式。最后,以马钢可分离债券为例进行实证分析,验证了本文得到的定价模型更合理。 相似文献
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Lyapunov exponents are studied for stochastic differential equations driven by Lévy processes. The transformation from stochastic differential equations to random integral equations and a multiplicative ergodic theorem are used. Moreover, the result is applied to physical and economic problems. 相似文献
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We consider a two-sided sequence of bounded operators in a Banach space which are not necessarily injective and satisfy two properties (SVG) and (FI). The singular value gap (SVG) property says that two successive singular values of the cocycle at some index d admit a uniform exponential gap; the fast invertibility (FI) property says that the cocycle is uniformly invertible on the fastest d-dimensional direction. We prove the existence of a uniform equivariant splitting of the Banach space into a fast space of dimension d and a slow space of codimension d. We compute an explicit constant lower bound on the angle between these two spaces using solely the constants defining the properties (SVG) and (FI). We extend the results obtained by Bochi and Gourmelon in the finite-dimensional case for bijective operators and the results obtained by Blumenthal and Morris in the infinite dimensional case for injective norm-continuous cocycles, in the direction that the operators are not required to be globally injective, that no dynamical system is involved and no compactness of the underlying system or smoothness of the cocycle is required. Moreover we give quantitative estimates of the angle between the fast and slow spaces that are new even in the case of finite-dimensional bijective operators in Hilbert spaces. 相似文献
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Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation 下载免费PDF全文
Convergence analysis is presented for recently proposed multistep schemes,
when applied to a special type of forward-backward stochastic differential equations (FBSDEs)
that arises in finance and stochastic control. The corresponding $k$-step scheme admits
a $k$-order convergence rate in time, when the exact solution of the forward stochastic
differential equation (SDE) is given. Our analysis assumes that the terminal conditions
and the FBSDE coefficients are sufficiently regular. 相似文献
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An approach is developed for the numerical solution of random vibration problems. It is based on treating random variables as functions in a certain Hilbert space. Stochastic processes are described as curves defined in this space, and concepts from deterministic approximation theory are applied to represent the solution as a series involving a known basis of stochastic processes, and a set of unknown coefficients which are deterministic functions of time. Then, a Galerkin projection procedure is utilized to derive a set of ordinary differential equations which can be solved numerically to determine the coefficients in the series. The versatility of the proposed approach is demonstrated by its application to a nonlinear vibration problem involving the probability density of a non-Markovian oscillator response. 相似文献
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Maryam Mohammadi Reza Mokhtari Hamid Panahipour 《Engineering Analysis with Boundary Elements》2013,37(12):1642-1652
The paper introduces a Galerkin method in the reproducing kernel Hilbert space. It is implemented as a meshless method based on spatial trial spaces spanned by the Newton basis functions in the “native” Hilbert space of the reproducing kernel. For the time-dependent PDEs it leads to a system of ordinary differential equations. The method is used for solving the 2D nonlinear coupled Burgers' equations having Dirichlet and mixed boundary conditions. The numerical solutions for different values of Reynolds number (Re) are compared with analytical solutions as well as other numerical methods. It is shown that the proposed method is efficient, accurate and stable for flow with reasonably high Re in the case of Dirichlet boundary conditions. 相似文献
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On Solution Regularity of Linear Hyperbolic Stochastic PDE Using the Method of Characteristics 下载免费PDF全文
Lizao Li 《East Asian journal on applied mathematics.》2012,2(3):266-276
The generalized Polynomial Chaos (gPC) method is one of the most widely
used numerical methods for solving stochastic differential equations. Recently, attempts
have been made to extend the the gPC to solve hyperbolic stochastic partial differential
equations (SPDE). The convergence rate of the gPC depends on the regularity of the
solution. It is shown that the characteristics technique can be used to derive general
conditions for regularity of linear hyperbolic PDE, in a detailed case study of a linear
wave equation with a random variable coefficient and random initial and boundary
data. 相似文献
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本文研究一类状态由随机微分方程确定的脉冲型随机控制的平稳问题,证明了最佳脉冲控制的存在性并得以具体刻画。 相似文献
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The investigation of a nonlinear stochastic delay equation with structural tool and regenerative time delays is presented. The conditions of Hopf bifurcation are computed in order to describe the regions of stability and instability. Explicit expressions characterizing the influence of nonlinear and stochastic perturbations, valid in the first order centre manifold approximation, are derived. In addition to this, we describe the underlying mathematical ideas of the centre manifold reduction of delay differential equations to ordinary differential equations for fixed time delays. 相似文献
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文基于随机动态规划原理与随机平均法,提出耦合相邻高耸结构的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型,再运用随机平均法导出关于模态能量的It6随机微分方程,应用随机动态规划原理建立动态规划方程,由此可确定最优控制律。将结构的响应控制化为模态能量控制,缩减控制系统的维数。用高斯随机过程模拟地震激励,可计及其功率谱特性。数值结果表明该耦合结构控制方法的有效性。 相似文献
20.
Henrik T Sykora Daniel Bachrathy Gabor Stepan 《International journal for numerical methods in engineering》2019,119(9):879-898
An efficient numerical method is presented to analyze the moment stability and stationary behavior of linear stochastic delay differential equations. The method is based on a special kind of discretization technique with respect to the past effects. The resulting approximate system is a high dimensional linear discrete stochastic mapping. The convergence properties of the method is demonstrated with the help of the stochastic Hayes equation and the stochastic delayed oscillator. 相似文献