\documentclass[12pt,a4paper]{article}


\begin{document}

\title{The Bock iteration for the ODE estimation problem
}
\author{M.R.Osborne \thanks{
Mathematical Sciences Institute, Australian National University,
ACT 0200, Australia}}
\date{}
\maketitle

\begin{abstract}
The Bock iteration provides a method for solving the ODE
estimation problem in its simultaneous form where the discretised
ODE is imposed as a system of constraints on the data fitting
problem. This system is potentially unbounded in size as the scale
of the discretization tends to 0. Constraints introduce Lagrange
multipliers into the necessary conditions, and it is necessary to
estimate them in order to carry out a convergence rate analysis.
The multipliers can be shown to be $O\left(n^{-1/2}\right),\;
n\to\infty$ where typically $n$ is the number of observations.
This estimate is obtained by interpreting the necessary conditions
as a discretization of a stochastic ODE system. It is necessary
also to take account of the unbounded size of the constraint
system by reducing the convergence rate questions to questions
involving consideration of a matrix of fixed dimension independent
of $n$.
\end{abstract}

\end{document}