The large deviation principle for a family of random variables is the following bound in essence . Nice application of this in stochastic volatility has been made for small maturities. The idea is to rescale the volatility diffusion
and rescale time and then apply the large deviation principle to . This is done in detail in Feng-Forde-Fouque-ShortMaturityAsymptoticsHeston-2010.
We want to consider the Heston model with replaced by a fractional Brownian motion with Hurst exponent and replicate the analysis. The scaling law for the fBM is . Therefore , and the correlation .
The transformation with a fractional Brownian motion that is uncorrelated with is not problematic