Journal of Economic Theory 122 (2005) 100–118 Stability of stochastic optimal growth models: a new approach Kazuo Nishimura a and John Stachurski b, a Institute of Economic Research, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan b Center for Operations Research and Econometrics, Universite´Catholique de Louvain, 34 Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium Received 2 February 2004; final version received 16 April 2004 Available online 17 June 2004 Abstract The paper proposes an Euler equation technique for analyzing the stability of differentiable stochastic programs. The main innovation is to use marginal reward directly as a Foster– Lyapunov function. This allows us to extend known stability results for stochastic optimal growth models, both weakening hypotheses and strengthening conclusions. r 2004 Elsevier Inc. All rights reserved. JEL classification: C61; C62; O41 Keywords: Optimal growth; Ergodicity; Law of Large Numbers; Central Limit Theorem 1. Introduction Many economic models are now explicitly dynamic and stochastic. Their state variables evolve in line with the decisions and actions of individual economic agents. These decisions are identified in turn by imposing rationality. Depending on technology, market structure, time discount rates and other primitives, rational behavior may lead either to stability or to instability. 1 ARTICLE IN PRESS  Corresponding author. E-mail addresses: nishimura@kier.kyoto-u.ac.jp (K. Nishimura), stachurski@core.ucl.ac.be (J. Stachurski). 1 Rationality itself has no intrinsic stability implications—any sufficiently smooth function can be rationalized as the solution to a discounted dynamic program [4]. 0022-0531/$-see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jet.2004.04.001