Abstract
The most powerful method in Chapter 5 was the “general compactness method” of Section 5.3. The basic assumption for that method is that the asymptotic “rate of change” of the martingale M 0(·) is zero with probability one. It was shown in Subsection 5.3.2 that the rate of change condition is quite weak and yields convergence under what are probably close to the weakest conditions on both the noise and step size sequences, when the underlying noise is of the martingale difference form. In this chapter it is shown that the same approach yields excellent results for correlated noise. General assumptions of the type used in Section 5.3 are stated in Subsection 1.1 and the main convergence theorem is proved in a straightforward way in Subsection 1.2.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kushner, H.J., Yin, G.G. (1997). Convergence with Probability One: Correlated Noise. In: Stochastic Approximation Algorithms and Applications. Applications of Mathematics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-2696-8_6
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2696-8_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-2698-2
Online ISBN: 978-1-4899-2696-8
eBook Packages: Springer Book Archive