This paper is concerned with the problem of the estimation of the integrated volatility of log-prices based on high frequency data when both price jumps and market microstructure noise are present. We begin by providing a survey of the leading estimators introduced in the literature to tackle...

We introduce LASSO-type regularization for large dimensional realized covariance estimators of log-prices. The procedure consists of shrinking the off-diagonal entries of the inverse realized covariance matrix towards zero. This technique produces covariance estimators that are positive definite...

We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S1. We obtain sharp results on the Hölder continuity in time of the paths of the solution . We then establish upper and lower bounds on hitting...