Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ODE Method and Spectral Theory of Markov Operators   We give a development of the ODE method for the analysis of recursive
algorithms described by a stochastic recursion. With variability modelled via
an underlying Markov process, and under general assumptions, the following
results are obtained: 1. Stability of an associated ODE implies that the
stochastic recursion is stable in a strong sense when a gain parameter is
small. 2. The range of gain-values is quantified through a spectral analysis of
an associated linear operator, providing a non-local theory. 3. A second-order
analysis shows precisely how variability leads to sensitivity of the algorithm
with respect to the gain parameter.
  All results are obtained within the natural operator-theoretic framework of
geometrically ergodic Markov processes.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex