非线性自回归序列的平稳解及其矩的存在性

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (2): 260-266.

• Articles • Previous Articles Next Articles

Stochastic Stability for the Nonlinear Autoregressive Series

ZHANG Ren, ZHANG Shao-Yi*

School of Mathematics and Computer Science, Hubei University, Wuhan 430062

Received:2011-05-25 Revised:2012-06-12 Online:2013-04-25 Published:2013-04-25
Contact: ZHANG Shao-Yi，zhshaoyi@yahoo.com.cn E-mail:zhangren29917@gmail.com; zhshaoyi@yahoo.com.cn
Supported by:
国家自然科学基金(10371032)和教育部博士点基金(20050512002)资助项目

In this paper, we discuss existence of the stationary distribution and moment of nonlinear autoregressive model with conditional heteroscedasticity by the Markov theory. Especially,only assume that random variable has density function in the innovation, but not positive
everywhere.

Key words: Markov chains, Nonlinear autoregressive, Uniform countable additivity

CLC Number:

60J20

Cite this article

ZHANG Ren, ZHANG Shao-Yi. Stochastic Stability for the Nonlinear Autoregressive Series[J].Acta mathematica scientia,Series A, 2013, 33(2): 260-266.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2013/V33/I2/260

Trendmd

References

[1] 金阳, 安鸿志. 非线性自回归序列的矩的存在.应用数学学报, 2006, 29(1): 1--8

[2] Liu J, Susko E. On strict stationary and ergodicy of a non-linear ARMA model. J Appl Probab, 1992, 29: 363--373

[3] Fonseca G, Tweedie R L. Stationary measures for non-irreducible non-continuous Morkov chains with time series application. Statistica Sinica, 2002, 12n(2): 651--660

[4] Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability. London: Springer-Verlag, 1993

Related Articles 9

[1]	Zhu Zhifeng, Zhang Shaoyi. Study on the Convergence of Nonhomogeneous Markov Chains with Probability Distance [J]. Acta mathematica scientia,Series A, 2018, 38(5): 963-969.
[2]	Zhang Ren, Zhang Shaoyi. The Existence of Invariant Measure for Markov Chains with Uniform Countable Additivity [J]. Acta mathematica scientia,Series A, 2018, 38(2): 350-357.
[3]	WAN Cheng-Gao. The Limit Theorems for Function of Markov Chains in Random Environments [J]. Acta mathematica scientia,Series A, 2015, 35(1): 163-171.
[4]	LI Ying-Qiu, WANG He-Song, WANG Zhong. Some Strong Limit Theorems of Geometric Average of Transition Probabilities \|and Their Function for Markov Chains in Markovian Environments [J]. Acta mathematica scientia,Series A, 2011, 31(2): 508-517.
[5]	HU Di-He. An Introduction to Markov Process in Random Environment [J]. Acta mathematica scientia,Series A, 2010, 30(5): 1210-1241.
[6]	Yang Weiguo. A Class of Small Deviation Theorems for the Sequences of N-valued Random Variables with Respect to mth-order Nonhomogeneous Markov Chains [J]. Acta mathematica scientia,Series A, 2009, 29(2): 517-527.
[7]	XIAO Zheng-Yan, HU Di-He. The Classification of States for Skew Product Markov Chains [J]. Acta mathematica scientia,Series A, 2003, 23(3): 306-313.
[8]	Yang Weiguo, Liu Kaidi, Dong Wei. The Convergence of The Cesaro Averages and The Strong Law of Large Numbers for Nonhomogeneous Markov Chains [J]. Acta mathematica scientia,Series A, 1998, 18(S1): 27-34.
[9]	Liu Jiakun, Lai Xuejian. The Converse to the Mean Value Theorem for Harmonic Functions and Harmonic Measure [J]. Acta mathematica scientia,Series A, 1997, 17(1): 90-94.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Yang Piwen. THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1057 .
[2]	Xu Yumei. BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1089 .
[3]	Chen Xuegang; Sun Liang; Xing Huaming. Paired-domination Number in Cubic Graphs[J]. Acta mathematica scientia,Series A, 2007, 27(1): 166 -170 .
[4]	Wei Xiao;Yu Jinyou; Hu Yijun. Large Deviations and Finite Time Ruin Probability for Perturbed Risk Model with Variable Premium Rate[J]. Acta mathematica scientia,Series A, 2007, 27(4): 616 -623 .
[5]	Zhang Wenzhuan;Tang Niansheng ; Wang Xueren. Confidence Regions in Nonlinear Reproductive Dispersion Mixed Models in Terms of Curvatures[J]. Acta mathematica scientia,Series A, 2006, 26(4): 547 -558 .
[6]	Shang Lina; Gao Zongsheng. The Growth of Entire Functions of Infinte Order Represented by Laplace-Stieltjes Transformation [J]. Acta mathematica scientia,Series A, 2007, 27(6): 1035 -1043 .
[7]	Su Hong; Zhao Zhenhua; Qiu Dunyuan. On Some p⁶-Groups with p-Groups as Automorphism Groups[J]. Acta mathematica scientia,Series A, 2008, 28(5): 937 -941 .
[8]	LibingHuang ; Mo Xiaohuan. On the Construction of {\boldmath $p$}-harmonic Morphisms[J]. Acta mathematica scientia,Series A, 2008, 28(2): 232 -239 .
[9]	Chen Li. Multivalued Solutions of an Iterative Equation[J]. Acta mathematica scientia,Series A, 2008, 28(4): 636 -642 .
[10]	SONG Yi-Sheng, YANG Chang-Sen. Solving Variational Inequality with Weak Contraction by Using Viscosity Approximation Methods[J]. Acta mathematica scientia,Series A, 2009, 29(3): 656 -668 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP