外汇市场波动在有界复平面上的随机游走
Foreign exchange market fluctuations as random walk in demarcated complex plane
摘要：
我们表明，随时间变化的波动$\{Δx\}$在外汇汇率准确地描述了一个复杂的平面，分为增益（+）和损失（-）部门的随机游走。$\{Δx\}$是$N$从原点随机步进的结果，而$|Δx|$是最终第$N$步位置的欧几里得距离的平方。$\{Δx(t)\}$的符号由平面中的第$N$步位置设置。该模型不仅解释了G7市场$\{Δx\}$的概率密度的指数统计，而且还解释了其观察到的不对称性，以及随时间延迟增加而变宽的幂律依赖性。
英文摘要：
We show that time-dependent fluctuations $\{Δx\}$ in foreign exchange rates are accurately described by a random walk in a complex plane that is demarcated into the gain (+) and loss (-) sectors. $\{Δx\}$ is the outcome of $N$ random steps from the origin and $|Δx|$ is the square of the Euclidean distance of the final $N$-th step position. Sign of $\{Δx(t)\}$ is set by the $N$-th step location in the plane. The model explains not only the exponential statistics of the probability density of $\{Δx\}$ for G7 markets but also its observed asymmetry, and power-law dependent broadening with increasing time delay.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
