On the global asymptotic stability and oscillation of solutions in a stochastic business cycle model. (English) Zbl 1390.39035
Summary: We discuss a second order nonlinear stochastic difference equation which is constructed of a business cycle model with organized labor considered. A global asymptotic mean square stability criterion is obtained by Lyapunov function method. We also prove a theorem on the almost sure oscillation of the solutions for the difference equation with state-independent stochastic perturbations.
MSC:
39A21 | Oscillation theory for difference equations |
39A50 | Stochastic difference equations |
60F15 | Strong limit theorems |
91B64 | Macroeconomic theory (monetary models, models of taxation) |
60B10 | Convergence of probability measures |
60G50 | Sums of independent random variables; random walks |
91B70 | Stochastic models in economics |
References:
[1] | DOI: 10.3934/dcds.2006.15.843 · Zbl 1115.39008 · doi:10.3934/dcds.2006.15.843 |
[2] | DOI: 10.1080/10236190802495303 · Zbl 1198.39032 · doi:10.1080/10236190802495303 |
[3] | DOI: 10.1007/BF00533478 · Zbl 0298.60015 · doi:10.1007/BF00533478 |
[4] | DOI: 10.1080/10236191003730548 · Zbl 1244.39017 · doi:10.1080/10236191003730548 |
[5] | Hicks J.R., A contribution to the theory of the trade cycle, 2. ed. (1965) |
[6] | DOI: 10.2307/1907075 · Zbl 0063.02946 · doi:10.2307/1907075 |
[7] | DOI: 10.1080/10236190410001652829 · Zbl 1072.39007 · doi:10.1080/10236190410001652829 |
[8] | DOI: 10.1080/10236190701483145 · Zbl 1141.39006 · doi:10.1080/10236190701483145 |
[9] | DOI: 10.1002/jae.3950070405 · doi:10.1002/jae.3950070405 |
[10] | DOI: 10.2307/1927758 · doi:10.2307/1927758 |
[11] | DOI: 10.1016/S0362-546X(96)00054-5 · Zbl 0877.39004 · doi:10.1016/S0362-546X(96)00054-5 |
[12] | Shaikhet L.E., Dynam. Systems Appl. 4 (2) pp 199– (1995) |
[13] | DOI: 10.1016/S0895-7177(02)00168-1 · Zbl 1029.93057 · doi:10.1016/S0895-7177(02)00168-1 |
[14] | DOI: 10.2307/1907851 · Zbl 0046.37803 · doi:10.2307/1907851 |
[15] | DOI: 10.1186/1687-1847-2014-91 · Zbl 1346.60036 · doi:10.1186/1687-1847-2014-91 |
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