Title

Stochastic Stability in Monotone Economies

Abstract

This paper presents new order-theoretic conditions for global stability of monotone Markov processes with possibly non-compact state spaces. Our main result shows that a Markov process induced by a continuous and increasing transition law is globally stable if it admits a Lyapunovlike function, and becomes larger than any given element of the state space with positive probability, or smaller than any given element of the state space with positive probability. This result applies to a wide range of stochastic economic models.

Keywords: Monotonicity, stability, Markov process, stochastic dynamics

Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: (81) 78 803 7036
Fax: (81) 78 803 7059

John STACHURSKI
Research School of Economics, Australian National University