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The ODE method and spectral theory of Markov operators
 IN STOCHASTIC THEORY AND CONTROL (LAWRENCE, KS, 2001), SER. LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES
, 2002
"... We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modeled via an underlying Markov process, and under general assumptions, the following results are obtained: (i) Stability of an associated ODE implies that the stoc ..."
Abstract

Cited by 11 (3 self)
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We give a development of the ODE method for the analysis of recursive algorithms described by a stochastic recursion. With variability modeled via an underlying Markov process, and under general assumptions, the following results are obtained: (i) Stability of an associated ODE implies that the stochastic recursion is stable in a strong sense when a gain parameter is small. (ii) The range of gainvalues is quantified through a spectral analysis of an associated linear operator, providing a nonlocal theory, even for nonlinear systems. (iii) A secondorder analysis shows precisely how variability leads to sensitivity of the algorithm with respect to the gain parameter. All results are obtained within the natural operatortheoretic framework of geometrically ergodic Markov processes.
Cycle time of stochastic maxplus linear systems
 Electronic Journal of Probability
, 2008
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