Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming
Bounding Stationary Averages of Polynomial Diffusions via Semidefinite Programming
复制标题
通过半定规划多项式扩散的有界平稳平均值
DOI：
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复制
发表时间：
2016
影响因子：
3.1
通讯作者：
Mauricio Barahona
中科院分区：
文献类型：
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作者：
Juan Kuntz;M. Ottobre;G. Stan;Mauricio Barahona
本文介绍了一种基于半定规划的算法，该算法的产生率是递增的。递减)较低的序列(分别为具有多项式漂移向量和扩散系数的扩散的多项式平稳平均值的上界。通过在由扩散的任何平稳度量的矩所满足的某些线性等式和半定不等式所定义的实向量集上优化由感兴趣的平稳平均值确定的目标来获得边界。我们通过几个应用来举例说明该方法的使用：贝叶斯推理问题；受乘性白噪声扰动的线性常微分方程李雅普诺夫指数的计算；以及来自结构力学的可靠性问题。此外，我们还证明了与Lyapunov指数计算有关的某些偏微分方程解的界收敛到平稳平均集的下确界和上确界，并在更一般的条件下给出了收敛的数值证据。
We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusions with polynomial drift vector and diffusion coefficients. The bounds are obtained by optimising an objective, determined by the stationary average of interest, over the set of real vectors defined by certain linear equalities and semidefinite inequalities which are satisfied by the moments of any stationary measure of the diffusion. We exemplify the use of the approach through several applications: a Bayesian inference problem; the computation of Lyapunov exponents of linear ordinary differential equations perturbed by multiplicative white noise; and a reliability problem from structural mechanics. Additionally, we prove that the bounds converge to the infimum and supremum of the set of stationary averages for certain SDEs associated with the computation of the Lyapunov exponents, and we provide numerical evidence of convergence in more general settings.
多项式跳跃扩散模型中双障碍合约定价的矩量法
DOI：
10.1142/s0219024911006644
发表时间：
2012
影响因子：
0.5
作者：
ERIKSSON B
通讯作者：
ERIKSSON B