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Mean stability of a stochastic difference equation. (English) Zbl 1141.37037

Summary: A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, but not the techniques for obtaining its properties, and we make use of the theory of abstract Banach algebras and weighted spaces. We hope that our study will lead to more realistic random models.

MSC:

37N40 Dynamical systems in optimization and economics
37H10 Generation, random and stochastic difference and differential equations
93E15 Stochastic stability in control theory
60G50 Sums of independent random variables; random walks
91B62 Economic growth models
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