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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Existence of stationary distributions for a class of nonlinear time series models in random environment domain | Wang et al. Journal of Inequalities and Applications 2011 2011 63 http www.journalofinequalitiesandapplications.eom content 2011 1 63 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Existence of stationary distributions for a class of nonlinear time series models in random environment domain Yueheng Wang 1 Enwen Zhu1 and Yong Xu2 Correspondence engwenzhu@126.com 1School of Mathematics and Computational Science Changsha University of Science and Technology 410076 Hunan China Full list of author information is available at the end of the article Springer Abstract In this paper we study the problem of a variety of nonlinear time series model Xn 1 F Xn en 1 Zn 1 in which Zn 1 is a Markov chain with finite state space and for every state i of the Markov chain en i is a sequence of independent and identically distributed random variables. Also the existence of the stationary distribution of the sequence Xn defined by the above model is investigated. Some new novel results on the underlying models are presented. 2010 Mathematics Subject Classification 60J10 Keywords Stationary distribution Nonlinear time series Random environment 1 Introduction It is known that stochastic difference equations provide models that represent a broad class of discrete-time stochastic systems and a unified representation leads to the following general model see e.g. 1-6 Xn 1 F Xn en 1 n 0 1.1 where F Rq X Rq Rq is a Boreal measurable mapping en is a sequence of independent and identically distributed q-dimensional random vectors on a probability space F P . It can be seen that sequence Xn defined in 1.1 forms a temporally homogeneous Markov chain with state space Rq Bq whenever X0 is a random variable on F P which is independent of en see e.g. 1-4 . It has been recognized that the application of model 1.1 is of great significance. However the limitations of the model are obvious that is it neglects the factor that interference with a system is affected by .
