关于具有长时间依赖的离散随机过程
On discrete stochastic processes with long-lasting time dependence
摘要：
在这篇手稿中，我们分析和数值研究的统计性质的heteroskedastic过程的基础上，著名的随机变量的方差是由记忆定义的$q_{m}$ -指数，形式（$e_{q_{m}=1}^{x}=e^{x}$）的随机生成器。具体而言，我们检查平方随机变量的自关联函数以及峰度。此外，通过数值计算，我们推导出了异方差随机变量和方差的平稳概率密度函数，多尺度性质，首次通过时间分布和依赖度。最后，我们引入了该模型的非对称方差版本，使我们能够重现金融市场中所谓的杠杆效应。
英文摘要：
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of $q_{m}$-exponencial, form ($e_{q_{m}=1}^{x}=e^{x}$). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.
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。
