Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-15T23:10:35.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Submartingales and stochastic stability

Published online by Cambridge University Press:  17 April 2009

Phil Diamond
Phil Diamond
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Sufficient conditions, involving the existence of a Lyapunov function which is a submartingale of special type, are given for the instability of stochastic discrete time systems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 2 , April 1974 , pp. 271 - 276
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Bucy, R.S., “Stability and positive supermartingales”, J. Differential Equations 1 (1965), 151–155.CrossRefGoogle Scholar
[2]Hahn, Wolfgang, Stability of motion (translated by Baartz, Arne P.. Die Grundlehren der mathematischen Wissenschaften, Band 138. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[3]Kalman, R.E. and Bertram, J.E., “Control system analysis and design via the “second method” of Lyapunov. II. Discrete-time systems”, Trans. ASME Ser. D. J. Basic Engrg. 82 (1960), 394–400.CrossRefGoogle Scholar
[4]Kendall, Maurice G. and Stuart, Alan, The advanced theory of statistics. Volume 1, Distribution theory, 2nd ed. (Charles Griffin, London, 1963).Google Scholar
[5]Kushner, Harold J., “On the stability of stochastic dynamical systems”, Proc. Nat. Acad. Sci. USA 53 (1960), 394–400.Google Scholar
[6]Loève, Michel, Probability theory: foundations, random sequences, 2nd ed. (Van Nostrand, New York, Toronto, London, 1960).Google Scholar