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Some Stability Results for Markovian Economic Semigroups

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Author Info

  • Leonard J. Mirman
  • Kevin Reffett
  • John Stachurski

Abstract

The paper studies existence, uniqueness and stability of stationary equilibrium distributions in a class of stochastic dynamic models common to economic analysis. The stability conditions provided are suitable for treating multi-sector models and nonlinear time series models with unbounded state.

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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 902.

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Length: 21 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:mlb:wpaper:902

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Postal: Department of Economics, The University of Melbourne, 4th Floor, FBE Building, Level 4, 111 Barry Street. Victoria, 3010, Australia
Phone: +61 3 8344 5355
Fax: +61 3 8344 6899
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Web page: http://www.economics.unimelb.edu.au
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Related research

Keywords: Markov processes; asymptotic stability; semigroups;

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References

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  1. Donaldson, John B. & Mehra, Rajnish, 1983. "Stochastic growth with correlated production shocks," Journal of Economic Theory, Elsevier, vol. 29(2), pages 282-312, April.
  2. Farmer, Roger E.A. & Woodford, Michael, 1997. "Self-Fulfilling Prophecies And The Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 1(04), pages 740-769, December.
  3. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  4. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer, vol. 28(1), pages 1-23, 05.
  5. Lisa Morhaim & Charles-Henri Dimaria & Cuong Le Van, 2002. "The discrete time version of the Romer model," Economic Theory, Springer, vol. 20(1), pages 133-158.
  6. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics 381, Boston College Department of Economics.
  7. Stachurski, John, 2003. "Economic dynamical systems with multiplicative noise," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 135-152, February.
  8. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  9. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
  10. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  11. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
  12. Razin, Assaf & Yahav, Joseph A, 1979. "On Stochastic Models of Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 599-604, October.
  13. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  14. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  15. Rabi Bhattacharya & Mukul Majumdar, 2003. "Dynamical systems subject to random shocks: An introduction," Economic Theory, Springer, vol. 23(1), pages 1-12, December.
  16. repec:cup:macdyn:v:1:y:1997:i:4:p:740-69 is not listed on IDEAS
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Citations

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Cited by:
  1. Costas Aariadis & John Stachurski, 2004. "Poverty Traps," Department of Economics - Working Papers Series 913, The University of Melbourne.
    • Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 5 Elsevier.

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