Stochastic Stability in Monotone Economies
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
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Research School of Economics, Australian National University