Abstract
The martingale method is a powerful tool for analyzing recursive identification algorithms and stochastic adaptive control systems. In this chapter, we first present classical convergence theorems for martingales [Do], [Cho], [St], [N], [LSh]. Then we estimate the sums of martingale difference sequence with single- and double-indexed random weights [St], [LW1], [CG3], [GHH], [HG]. These results are the bases of analysis for the least-square-based estimates for coefficients and orders which will be considered in later chapters.
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© 1991 Springer Science+Business Media New York
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Han-Fu, C., Guo, L. (1991). Limit Theorems on Martingales. In: Identification and Stochastic Adaptive Control. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0429-9_2
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DOI: https://doi.org/10.1007/978-1-4612-0429-9_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6756-0
Online ISBN: 978-1-4612-0429-9
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