快速非线性均值回复过程的标度极限
Scaling Limits of Processes with Fast Nonlinear Mean Reversion
摘要：
我们得到了具有快速非线性均值回复速度的Itô过程的积分泛函的标度极限。我们表明，在这些限制，快速均值回复过程是“平均”的集成对它的不变测度。这些收敛结果在概率上一致成立，在较弱的可积性条件下，在$\mathcal{S}^p$中也一致成立。他们是一个重要的积木的投资组合选择模型的分析与小超线性交易成本，在本研究的配套文件进行。
英文摘要：
We derive scaling limits for integral functionals of Itô processes with fast nonlinear mean-reversion speed. We show that in these limits, the fast mean-reverting process is "averaged out" by integrating against its invariant measure. These convergence results hold uniformly in probability and, under mild integrability conditions, also in $\mathcal{S}^p$. They are a crucial building block for the analysis of portfolio choice models with small superlinear transaction costs, carried out in the companion paper of the present study.
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