Abstract
We derive scaling limits for integral functionals of Itô processes with fast nonlinear mean-reversion speeds. In these limits, the fast mean-reverting process is “averaged out” by integrating against its invariant measure. The convergence is uniformly in probability and, under mild integrability conditions, also in Sp. These results 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 [11].
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