Abstract
It is usually difficult to express a family of tri-point transition function (TTF) by a transition matrix as Markov processes with one parameter. In this paper, we define three kinds of connection matrixes on the states of standard tri-point transition function (STTF) and study their essential character, give a constructive method on the constant-value standard tri-point transition function and a general expression of the state-symmetric standard tri-point transition function by a sequence of the transition matrixes of special and simple Markov processes with one parameter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yang, X. Q., Li, Y. Q., Markov Processes With Two Parameters (in Chinese), Changsha: Hunan Science & Technology Press, 1996.
Guo, J. Y., Yang, X. Q., Three-point transition function for two-parameter Markov chains and their four systems of partial differential equations, Science in China, Series A, 1992, 35(7): 806–818.
Yang, X. Q., Wide-past homogeneous Markov processes with two parameters and two states, Chinese Science Bulletin (in Chinese), 1996, 41(2): 192.
Yang, X. Q., Markov properties for two-parameter stochastic processes with independent increaments and exitence of its family of three-point transition function, Annals of Mathematical Researches, 1993, 26(2): 1–5.
Li, Y. Q., Some properties of two-parameter stochastic processes with stationary independent increments in an origin, Journal of Mathematical Research and Exposition (in Chinese), 1996, 16(3): 455–460.
Liu, S. Y., Densty functions of three points transition functions of two-parameter Markov chains, Natural science journal of Xiangtan University (in Chinese), 1993, 15(3): 26–27.
Zhou, J. W., State space transform of Markov processes with two parameters, Science in China, Series A (in Chinese), 1996, 26(8): 677–682.
Yang, X. Q., The Construction Theory of Denumerable Markov Process (in chinese), Changsha: Hunan Science & Technology Press, 1981; John Wiley & Sons, 1990.
Wang, Z. K., Yang, X. Q., The Birth and Death Processes and Markov Chains, Beijing: Science Press, 1992.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yuquan, X. Standard tri-point transition function. Sci. China Ser. A-Math. 48, 904–914 (2005). https://doi.org/10.1007/BF02879073
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02879073