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Dimensions of Economic Theory and PolicyEssays for Anjan Mukherji$
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Krishnendu Ghosh Dastidar, Hiranya Mukhopadhyay, and Uday Bhanu Sinha

Print publication date: 2011

Print ISBN-13: 9780198073970

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780198073970.001.0001

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On Some Monotone Markov Models

On Some Monotone Markov Models

(p.35) 3 On Some Monotone Markov Models
Dimensions of Economic Theory and Policy

Mukul Majumdar

Nigar Hashimzade

Oxford University Press

This chapter presents some results and examples on the invariant distributions of monotone Markov processes. It summarizes the fundamental results on the existence, uniqueness, and stability of the invariant distribution for the Dubins-Freedman as well as Lindley-Spitzer processes. It also examines the speed of convergence. The derivation of the analytical properties of invariant distributions is known to be problematic. Majumdar and Hashimzade provide a concrete example of a class of Markov processes whereby it is possible to completely identify the unique invariant distribution. They also discuss the relevance of such processes in policies dealing with management of renewable resources that allows for (random) regeneration. This chapter considers a model that describes a policy of ‘constant harvesting’ or ‘constant yield’ in renewable resource management.

Keywords:   Markov processes, invariant distributions, Dubins-Freedman processes, Lindley-Spitzer processes, convergence, renewable resources, resource management, regeneration, constant harvesting, constant yield

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