共查询到20条相似文献,搜索用时 62 毫秒
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A. TOCINO 《BIT Numerical Mathematics》2007,47(1):189-196
A method for the numerical solution of stochastic differential equations is presented. The method has mean-square order equal
to 1/2 when it is applied to a general stochastic differential equation and equal to 1 if the equation has additive noise.
In addition, it is shown that the method captures some long-time properties of a linear stochastic oscillator: It reproduces
exactly the growth rate of the second moment and the oscillation property of the solution.
AMS subject classification (2000) 60H10, 34F05, 65U05, 60K40 相似文献
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我们主要构造了数值求解一类1指标随机延迟微分代数系统的Euler-Maruyama方法,并且证明用该方法求解此类问题可达到1/2阶均方收敛.最后的效值试验验证了方法的有效性及所获结论的正确性. 相似文献
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《随机分析与应用》2013,31(4):1085-1110
Abstract The mean-square filtering problem for the discrete Volterra equations is a nontrivial task due to an enormous amount of operations required for the implementation of optimal filter. A difference equation of a moderate dimension is chosen as an approximate model for the original system. Then the reduced Kalman filter can be used as an approximate but efficient estimator. Using the duality theory of convex variational problems, a level of nonoptimality for the chosen filter is obtained. This level can be efficiently computed without exactly solving the full filtering problem. 相似文献
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本文讨论一般非线性随机延迟微分方程Heun方法的数值稳定性,证明了如果问题本身满足零解是均方指数稳定和均方渐近稳定的充分条件,则当方程的漂移项进一步满足一定的条件时,Heun方法是Ms.稳定的,带线性插值的Heun方法是均方指数稳定的和GMS-稳定的理论结果.文末的数值试验进一步验证了所得的相关结论. 相似文献
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We deal with linear multi-step methods for SDEs and study when the numerical approximation shares asymptotic properties in
the mean-square sense of the exact solution. As in deterministic numerical analysis we use a linear time-invariant test equation
and perform a linear stability analysis. Standard approaches used either to analyse deterministic multi-step methods or stochastic
one-step methods do not carry over to stochastic multi-step schemes. In order to obtain sufficient conditions for asymptotic
mean-square stability of stochastic linear two-step-Maruyama methods we construct and apply Lyapunov-type functionals. In
particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams–Bashforth- and Adams–Moulton-methods,
the Milne–Simpson method and the BDF method.
AMS subject classification (2000) 60H35, 65C30, 65L06, 65L20 相似文献
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本文讨论Euler方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,利用了一种不同于以往文献中的证明技巧,给出了Euler方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable without noise, but can be made exponentially unstable in mean-square by a noise perturbation that shrinks to zero as the nonnormality increases. We then show via finite-time convergence theory that an Euler approximation shares the same property, giving a discrete analogue of the result. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65C30, 34F05 相似文献
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G.N. Milstein & M.V. Tretyakov 《高等学校计算数学学报(英文版)》2021,14(1):1-30
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time
subintervals resulting in a linear stochastic parabolic equation for vorticity. At each
time step, the velocity is expressed via vorticity using a formula corresponding to
the Biot-Savart-type law. We prove the first mean-square convergence order of the
vorticity approximation. 相似文献
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姚慧丽 《应用泛函分析学报》2011,13(1):30-35
利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性.在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论.从而得到的结果在一定程度上推广和改进了相关结果. 相似文献
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基因调控网络(GRNs)及其动力学模型的研究在后基因组时代是一个重要的研究领域.定性分析基因调控网络及其动力学对系统地认识生物体具有重要意义.该文提出了一类具有时变时滞和Markov切换的随机基因调控网络模型,研究了其均方同步和随机无源同步问题.通过设计合适的Lyapunov-Krasovskii泛函(LKF),并利用Lyapunov稳定性理论、线性矩阵不等式方法和随机分析技巧,得到了均方同步和随机无源同步的充分条件.此外,通过与其他文献进行比较,显示了该文结果的理论价值.数值模拟验证了所得充分条件的有效性. 相似文献
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In this article we present results of a linear stability analysis of stochastic linear multi-step methods for stochastic ordinary differential equations. As in deterministic numerical analysis we use a linear time-invariant test equation and study when the numerical approximation shares asymptotic properties in the mean-square sense of the exact solution of that test equation. Sufficient conditions for asymptotic mean-square stability of stochastic linear two-step-Maruyama methods are obtained with the aide of Lyapunov-type functionals. In particular we study the asymptotic mean-square stability of stochastic counterparts of two-step Adams-Bashforth- and Adams-Moulton-methods and the BDF method. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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研究了一类具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性.利用时变区间矩阵的分解技术、矩阵的Kronecker积的性质和Lyapunov函数法,得到了该系统均方鲁棒稳定的几个充分性条件.通过一个数值例子说明了所得的这些充分性条件的有效性和实用性. 相似文献
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Exponential stability of Euler-Maruyama solutions for impulsive stochastic differential equations with delay 总被引:1,自引:0,他引:1
This paper establishes a method to study the exponential stability of Euler-Maruyama (EM) method for impulsive stochastic differential equations with delay. By using the properties of M-matrix and stochastic analysis technique, some conditions under which the EM solution is exponentially mean-square stable are obtained. Some examples are provided to illustrate the results. 相似文献
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针对一类变延迟微分方程,应用全隐式方法一平衡方法,研究了其收敛性和稳定性.结果表明平衡方法以1/2 γ,γ∈(0,1]阶收敛到精确解;并且强平衡方法和弱平衡方法都能保持解析解的均方稳定性;进一步数值实验验证了算法理论分析的正确性,并且表明全隐式的平衡方法比显式方法—Euler方法具有更好的稳定性. 相似文献
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In this paper a family of fully implicit Milstein methods are introduced for solving stiff stochastic differential equations (SDEs). It is proved that the methods are convergent with strong order 1.0 for a class of SDEs. For a linear scalar test equation with multiplicative noise terms, mean-square and almost sure asymptotic stability of the methods are also investigated. We combine analytical and numerical techniques to get insights into the stability properties. The fully implicit methods are shown to be superior to those of the corresponding semi-implicit methods in term of stability property. Finally, numerical results are reported to illustrate the convergence and stability results. 相似文献