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Sample-Path Stability of Non-Stationary Dynamic Economic Systems

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  • Klaus Schenk-Hoppé

Abstract

The goal of this paper is to introduce and illustrate a new approach to the stability analysis of sample-paths of non-linear stochastic economic models with non-stationary components. We place our study within the mathematical theory of random dynamical systems and apply the concept of a random fixed point which is tailor-made for the study of the long-term behavior of sample-paths in stochastic systems. The main tool for the application of this approach is a Banach-type fixed point theorem for non-stationary random dynamical systems which is proved here. The concept and the theorem are thoroughly explained and illustrated by examples from stochastic growth theory. Copyright Kluwer Academic Publishers 2002

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  • Klaus Schenk-Hoppé, 2002. "Sample-Path Stability of Non-Stationary Dynamic Economic Systems," Annals of Operations Research, Springer, vol. 114(1), pages 263-280, August.
    • Handle: RePEc:spr:annopr:v:114:y:2002:i:1:p:263-280:10.1023/a:1021074506105
    DOI: 10.1023/A:1021074506105
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    1. Manjira Datta & Leonard J. Mirman, 2000. "Dynamic Externalities and Policy Coordination," Review of International Economics, Wiley Blackwell, vol. 8(1), pages 44-59, February.
    2. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
    3. Datta, Manjira & Mirman, Leonard J., 1999. "Externalities, Market Power, and Resource Extraction," Journal of Environmental Economics and Management, Elsevier, vol. 37(3), pages 233-255, May.
    4. Fischer, Ronald D. & Mirman, Leonard J., 1992. "Strategic dynamic interaction : Fish wars," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 267-287, April.
    5. Binder, Michael & Pesaran, M Hashem, 1999. "Stochastic Growth Models and Their Econometric Implications," Journal of Economic Growth, Springer, vol. 4(2), pages 139-183, June.
    6. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
    7. Binder, M. & Pesaran, M.H., 1996. "Stochastic Growth," Cambridge Working Papers in Economics 9615, Faculty of Economics, University of Cambridge.
    8. Mirman, Leonard J, 1972. "On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 271-286, June.
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    Cited by:

    1. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    2. Marten Hillebrand, 2008. "Pension Systems, Demographic Change, and the Stock Market," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-77972-8, December.

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    More about this item

    Keywords

    sample-path stability; random fixed points; non-stationary random dynamical systems;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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