论文标题
非线性马尔可夫链的收敛边界的估计和应用
Estimation and Application of the Convergence Bounds for Nonlinear Markov Chains
论文作者
论文摘要
非线性马尔可夫链（NMC）被视为具有非线性小扰动的原始（线性）马尔可夫链。它更适合现实世界数据，但是它相关的属性很难描述。提出了一种新的方法来分析终点性，甚至估计NMC的收敛范围，这比现有结果更精确。在新方法中，对马尔可夫的耦合马尔可夫耦合将应用于任何时间与限制分布之间的分布之间的关系。收敛边界可以通过耦合马尔可夫的过渡概率矩阵提供。此外，可以通过收敛范围，小波分析和高斯HMM来计算一种称为电视波动率的新波动率。经过测试以估计两种证券（TSLA和AMC）的波动性。结果表明，电视波动率可以反映出一个时期内正方形回报变化的大小。
Nonlinear Markov Chains (nMC) are regarded as the original (linear) Markov Chains with nonlinear small perturbations. It fits real-world data better, but its associated properties are difficult to describe. A new approach is proposed to analyze the ergodicity and even estimate the convergence bounds of nMC, which is more precise than existing results. In the new method, Coupling Markov about homogeneous Markov chains is applied to reconstitute the relationship between distribution at any times and the limiting distribution. The convergence bounds can be provided by the transition probability matrix of Coupling Markov. Moreover, a new volatility called TV Volatility can be calculated through the convergence bounds, wavelet analysis and Gaussian HMM. It's tested to estimate the volatility of two securities (TSLA and AMC). The results show TV Volatility can reflect the magnitude of the change of square returns in a period wonderfully.
