论文标题
随机动力学的几何形状千差线的数值计算
Numerical computations of geometric ergodicity for stochastic dynamics
论文作者
论文摘要
本文介绍了计算随机过程收敛几何速率的概率方法。目标是定量计算收敛速率与随机过程不变概率度量的上限和下限。通过应用耦合方法，我们得出了一种不需要离散状态空间的算法。通过这种方式，我们的方法在许多高维实例中都很好。我们将此算法应用于随机扰动的迭代映射和随机微分方程。我们表明，随机扰动系统的几何层状速率在某种程度上可以揭示出未扰动的确定性的混乱特性。还探索了各种SDE模型，包括具有退化噪声或高维状态空间的模型。
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the invariant probability measure of a stochastic process. By applying the coupling method, we derive an algorithm which does not need to discretize the state space. In this way, our approach works well for many high-dimensional examples. We apply this algorithm to both random perturbed iterative mappings and stochastic differential equations. We show that the rate of geometric ergodicity of the random perturbed system can, to some extent, reveal the chaotic properties of the unperturbed deterministic one. Various SDE models including those with degenerate noise or high-dimensional state space are also explored.
