In this paper, we proved the almost sure limit theorems for the maxima of stochastic volatility models with both light-tailed and heavy-tailed noises, where the volatility sequence is a log-Gaussian linear process. For the light-tailed noise case, we assume that the autocorrelation function $r_n$ of the Gaussian linear process satisfies $r_n\ln n(\ln \ln n{)}^{1+\epsilon }=O(1)$ for some $\epsilon >0$. For the heavy-tailed noise case, we assume that the Gaussian linear process is strong mixing with mixing rate $\gamma (n)$ satisfying $\gamma (n)(\ln \ln n{)}^{1+\epsilon }=O(1)$ for some $\epsilon >0$.

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随机波动率模型的最大值的几乎确定极限定理

在本文中，我们证明了具有轻尾和重尾噪声的随机波动率模型的最大值的几乎确定的极限定理，其中波动率序列是对数-高斯线性过程。对于轻尾噪声情况，我们假设自相关函数${\mathrm{[R}}_{ñ}$ 高斯线性过程满足 ${\mathrm{[R}}_{ñ}\ln ñ（\ln \ln ñ{）}^{\mathrm{1个}+\epsilon }=Ø（\mathrm{1个}）$ 对于一些 $\epsilon >0$。对于重尾噪声情况，我们假设高斯线性过程是具有混合速率的强混合$\gamma （ñ）$ 满意的 $\gamma （ñ）（\ln \ln ñ{）}^{\mathrm{1个}+\epsilon }=Ø（\mathrm{1个}）$ 对于一些 $\epsilon >0$。