How to structure the topology of a neural net (the hyper-parameters optimization) is a recurring problem of crucial importance for both the quality and rapidity of the learning process, which will be then translated onto the final outputs.In this paper we investigate a smart two-step procedure...

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...