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Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models

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Author Info

  • Christian Bayer

    ()
    (Department of Mathematics, University of Vienna, Austria)

  • Klaus Waelde

    ()
    (Department of Economics, Johannes Gutenberg-Universitaet Mainz, Germany)

Abstract

We study a dynamic stochastic general equilibrium model in continuous time. Related work has proven that optimal consumption in this model is a smooth function of state variables. This allows us to describe the evolution of optimal state variables (wealth and labour market status) by stochastic differential equations. We derive conditions under which an invariant distribution for state variables exists and is unique. We also provide conditions such that initial distributions converge to the long-run distribution.

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File URL: http://www.macro.economics.uni-mainz.de/RePEc/pdf/Discussion_Paper_1111.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz in its series Working Papers with number 1111.

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Length: 36 pages
Date of creation: 21 Jul 2011
Date of revision: 21 Jul 2011
Handle: RePEc:jgu:wpaper:1111

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Keywords: uncertainty in continuous time; Poisson process; existence; uniqueness; stability;

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