论文标题
多元几何布朗运动的截止稳定性
Cutoff stability of multivariate geometric Brownian motion
论文作者
论文摘要
本文建立了三个用于多变量（Hurwitz）稳定的几何布朗尼运动的三个统计数量的临界融合或突然收敛：自相关函数，当前状态及其退化限制度量之间的瓦斯泰因距离，最终，使用反合量的量子量，均可在跨量的速率之间进行跨性别率，从而产生了跨量的速率，从而构成了跨量的速度。 Borel-cantelli引理。在同时具有对角的漂移和波动率矩阵的情况下，我们获得了均方根的完整表示，并得出了非平凡，充分和必要的均方根稳定性条件，其中包括挥发性矩阵光谱的所有真实和虚构部分。
This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation function, the Wasserstein distance between the current state and its degenerate limiting measure, and, finally, anti-concentration probabilities, which yield a fine-tuned trade-off between almost sure rates and the respective integrability of the random modulus of convergence using a quantitative Borel--Cantelli Lemma. We obtain in case of simultaneous diagonalizable drift and volatility matrices a complete representation of the mean square and derive nontrivial, sufficient and necessary mean square stability conditions, which include all real and imaginary parts of the volatility matrices' spectra.
