On Lipschitz continuity of the iterated function system in a stochastic optimal growth model
AbstractThis paper provides qualitative properties of the iterated function system (IFS) generated by the optimal policy function for a class of stochastic one-sector optimal growth models. We obtain, explicitly in terms of the primitives of the model (i) a compact interval (not including the zero stock) in which the support of the invariant distribution of output must lie, and (ii) a Lipschitz property of the iterated function system on this interval. As applications, we are able to present parameter configurations under which (a) the support of the invariant distribution of the IFS is a generalized Cantor set, and (b) the invariant distribution is singular.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
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Stochastic optimal growth Iterated function system Invariant measure Lipschitz property Contraction property No overlap property Generalized topological Cantor set Singular invariant distribution;
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