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

Christian Bayer () and Klaus Waelde ()
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Christian Bayer: Department of Mathematics, University of Vienna, Austria
Klaus Waelde: Department of Economics, Johannes Gutenberg-Universitaet Mainz, Germany
Authors registered in the RePEc Author Service: Klaus Wälde

No 1111, Working Papers from Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz

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.

Keywords: uncertainty in continuous time; Poisson process; existence; uniqueness; stability (search for similar items in EconPapers)
JEL-codes: C62 D91 E24 J63 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2011-07-21, Revised 2011-07-21
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https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_1111.pdf First version, 2011 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:jgu:wpaper:1111

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