随机波动模型最大值的极限定理

Limit theorems for the maxima of stochastic volatility models

考虑一类经典的随机波动模型,其波动性由平稳的对数高斯随机序列进行刻画.假设该高斯随机序列相关系数函数rn满足lim_(n→∞)rnln_(n)=r∈[0,∞],利用点过程的相关方法,证明了几个关于该随机波动模型最大值及次序统计量的极限定理,推广了文献中存在的一些经典结论.

In this paper,by using the method of point process,several weak limit theorems for the maxima and order statistics of stochastic volatility models are proved,in which the logarithm of the volatility sequence is a Gaussian process with correlation function rn satisfying the condition that lim_(n→∞)r_(n)ln n=r∈[0,∞].The obtained results extend those existing in the literatures.