Stein’s method for nonconventional sums

Nonconventional Method of Polymer Patterning

Steins method, Malliavin calculus and infinite-dimensional Gaussian analysis

This expository paper is a companion of the four one-hour tutorial lectures given in the occasion of the special month Progress in Stein’s Method, held at the University of Singapore in January 2009. We will explain how one can combine Stein’s method with Malliavin calculus, in order to obtain explicit bounds in the normal and Gamma approximation of functionals of in…nite-dimensional Gaussian …...

The Resonance Method for Large Character Sums

We consider the size of large character sums, proving new lower bounds for ∆(N, q) = supχ6=χ0 mod q | ∑ n<N χ(n)| in almost all ranges of N . The proofs use the resonance method and saddle point analysis.

Nonconventional Limit Theorems in Averaging

We consider ”nonconventional” averaging setup in the form dX(t) dt = ǫB ` X(t), ξ(q1(t)), ξ(q2(t)), ..., ξ(ql(t)) ́ where ξ(t), t ≥ 0 is either a stochastic process or a dynamical system (i.e. then ξ(t) = F x) with sufficiently fast mixing while qj(t) = αjt, α1 < α2 < ... < αk and qj , j = k+1, ..., l grow faster than linearly. We show that the properly normalized error term in the ”nonconventio...

Ensemble Assimilation of Nonconventional Observations for Nowcasting

The final goal of this project is to provide the US Navy with an increased capability of using Doppler radar observations in the detection and prediction of hazardous weather events that usually have a strong randomness in nature and affect the Navy operations, especially over oceans and in remote areas. By developing a high-resolution data assimilation capability that can effectively assimilat...