We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchy in d dimensions, for focusing and defocusing interactions. We give a new proof of local well-posedness which avoids any high order Duhamel expansions, in contrast to previous proofs. Instead, we establish a new Strichartz estimate on the free evolution for GP hierarchies, and develop a T −T ∗ type argument, which, in turn, makes ...

let be a stationary sequence of pair wise negative quadrant dependent random variables with survival function {,1}nxn?f(x)=p[x>x]. the empirical survival function ()nfx based on 12,,...,nxxx is proposed as an estimator for ()nfx. strong consistency and point wise as well as uniform of ()nfx are discussed