Pathwise stability of likelihood estimators for diffusions via rough paths

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise stability properties as well as robustness toward misspecification in volatility and even the very nature of the noise. Two numerical examples demonstrate the practical relevance of our results.Comment: Published at http://dx.doi.org/10.1214/15-AAP1143 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cancellation of Glauber gluon exchange in the double Drell-Yan process

An essential part of any factorisation proof is the demonstration that the exchange of Glauber gluons cancels for the considered observable. We show this cancellation at all orders for double Drell-Yan production (the double parton scattering process in which a pair of electroweak gauge bosons is produced) both for the integrated cross section and for the cross section differential in the transverse boson momenta. In the process of constructing this proof, we also revisit and clarify some issues regarding the Glauber cancellation argument and its relation to the rest of the factorisation proof for the single Drell-Yan process.Comment: 65 pages, 23 figure