Title: A weak law of large numbers for estimating the correlation in bivariate Brownian semistationary processes,
Abstract: This article presents various weak laws of large numbers for the so-called
realised covariation of a bivariate stationary stochastic process which is not
a semimartingale. More precisely, we consider two cases: Bivariate moving
average processes with stochastic correlation and bivariate Brownian
semistationary processes with stochastic correlation. In both cases, we can
show that the (possibly scaled) realised covariation converges to the
integrated (possibly volatility modulated) stochastic correlation process.