一类定常非线性随机差分方程平稳解的存在性

Existence of stationary Dsitributions for a Class of Time-Invariant Nonlinear Stochastic Difference Equations

本文首先给出了由一般形式广义Ｋａｐｌａｎ条件表述的关于一般状态马氏链不存在平稳分布的一个充分条件，并放宽了对马氏链本身ψ－不可约性的条件要求；其次，对一类定常非线性随机差分方程平稳解及其矩的存在性问题进行了讨论；最后，对一类具有无限容量的随机库存模型，分析了其平稳分布的存在性问题．

One sufficient condition for nonexistence of stationary distribution of general state Markovchains is presented in terms of a more generalized Kaplan’s condition and with no irreducibilityassumptions.Then the existence of stationary distributions and moments for a c]ass of time-invariantnonlinear stochastic difference equations are discussed.Finally,stationary distributions existence for akind of stochastic dam models with infinite capacity are analyzed.