Necessary and sufficient conditions for the Robbins-Monro method

Efficient Robbins-Monro Procedure for Binary Data

The Robbins-Monro procedure does not perform well in the estimation of extreme quantiles, because the procedure is implemented using asymptotic results, which are not suitable for binary data. Here we propose a modification of the Robbins-Monro procedure and derive the optimal procedure for binary data under some reasonable approximations. The improvement obtained by using the optimal procedure...

The continuous dynamic Robbins-Monro procedure

Necessary and Sufficient Conditions for Copositive Tensors

In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal subtensors has no (non-positive) negative H++-eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of Z++-eigenvalues of the principal sub-tensors of that tensor. This presents a method for testing (strict) copositiv...

Necessary and sufficient conditions for quantum computation

Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer . The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived ; aspects of the transformation between the diagonal representation an...

Some necessary and sufficient conditions for Hypercyclicity

We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.