Derivative and approximation theorems on local fields

Negative Theorems on Monotone Approximation

Ergodic Theorems and Approximation Theorems with Rates

A-ergodic nets and A-regularized approximation processes of operators are introduced and their convergence theorems are discussed. There are strong convergence theorems, uniform convergence theorems, theorems on optimal convergence, and theorems on non-optimal convergence and its sharpness. The general results provide unified approaches to investigation of convergence rates of ergodic limits an...

Local convergence theorems for adaptive stochastic approximation schemes.

For the regression model y = M(x) + epsilon, adaptive stochastic approximation schemes of the form x(n+1) = x(n) - y(n)/(nb(n)) for choosing the levels x(1),x(2),... at which y(1),y(2),... are observed converge with probability 1 to the unknown root theta of the regression function M(x). Certain local convergence theorems that relate the convergence rate of x(n) - theta to the limiting behavior...

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities Nikolay Bliznyuk a , David Ruppert b & Christine A. Shoemaker c a Department of Statistics, University of Florida, Gainesville, FL, 32611 b School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, 14853 c School of Civil and Environmental Engineering, and School of Operations R...

ON LOCAL T ( b ) THEOREMS

We prove a local T (b) theorem for singular integral operators in the spirit of the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Thiele, Tao and the first author. The method consists in reducing one situation to the other by representing via the Beylkin-Coifman-Rokhlin algorithm any singular integral operator with truncated kernel as the sum of a bounded oper...