Dissertation > Excellent graduate degree dissertation topics show

Some Problems of Markov Chains in Random Environments

Author: LiuWei
Tutor: YangXiangQun
School: Hunan Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Markov chains Bi-infinite random environments Relativefrequency Strong limit Relative entropy density Branching process withimmigration
CLC: O211.62
Type: Master's thesis
Year: 2012
Downloads: 62
Quote: 0
Read: Download Dissertation

Abstract


In general, while doing the theoretical research for Markov chains in random environments, we generalize the existing results in the determine environments to the random environments. But many new concepts and new methods are created during the research, which is the essence of the theory of Markov chains in random environments.In this paper, the limit properties of the relative frequency of Markov chains in single infinite Markov environment are studied by the classic analytical methods-interval subdivision method. But there is difficulties in dealing with the corresponding problems of the double infinite Markov chains. In view of this, some limit properties of Markov source in bi-infinite random environments are given by constructing a nonnegative martingale which converges almost surely. One of the specific models of the Markov chains in random environments, that is branching process in random environments with immigration, is studied in this paper. We generalize the existing results in the Galton-Waston branching process with immigration to the branching process in random environments with immigration.In this paper, we obtain the following conclusions:1、The limit properties of relative frequency of markov chains in single infinite Markov environments are studied, and the upper (lower) bound of the upper (lower) limit is obtained.2、A strong limit theorem of the average of ternary functions for Markov chains in bi-infinite random environments is giving by constructing a nonnegative martingale which converges almost surely. As corollaries, some limit properties of relative entropy density of these chains are obtained, and the environment sequences are not required to be a Markov chains. The properties of Markov chain transition probability is studied, and the geometric average of the strong limit theorem represented by inequalities is obtained. As a corollary, the arithmetic average of the strong limit theorem represented by inequalities is obtained.3、The branching process in random environments with immigration is study. Under certain conditions, its total number of then generation individuals’conditional probability generating function converges to an appropriate stable distribution. Let Wn=Zn/Πf=0n-1mj, then there exists an integrable random variable W, makes Wn convergence to W, which converges almost surely and also according to the mean square.

Related Dissertations

  1. Some Strong Limit Theorems for Markov Chain Fields on a Tree,O211.4
  2. Some Strong Deviation Theorems for Markov Chain Fields on A Tree,O211.62
  3. A Mathematical Analysis for the Evolution of Public Goods Game under the Social Structure of Global Learning and Interaction,F062.6
  4. Markov chains in the use of biological networks,O157.5
  5. The Construction of Uni-lateral Birth and Death Process,O211.62
  6. Dual Branching q-Matrix and Its Application to Markov Integrated Semigroup,O211.63
  7. Analysis of Small-World Model to a Tendentious Ring Network,O157.5
  8. The Generalized Birth-death Catastrophes Process and Its Corresponding Markov Integrater Semigroup,O177
  9. L~2-concentration of Blow-up Solutions for Nonlinear Schr(?)dinger Equation,O175.24
  10. Some Asymptotic Properties of Randomized Design Based on Two Treatments,R311
  11. The Theory of Excursion of Markov Chains,O211.62
  12. Some Studies of One-Dimensional Random Walks in Romdom Environments,O211.6
  13. On Direct Convergence and Ergodic Theorem of Markov Chains in Random Environments,O211.6
  14. Some Stong Limit Theorems and Its Application to the Even-Odd Markov Chain Fields Indexed by a Extended Bethe Tree,O171
  15. Some Properties of Random Walks in Random Environments,O211
  16. A special class of non-homogeneous Markov Chain Fields tree limit properties,O211.6
  17. Multi-level Models and Algorithms for Evaluating Operational Reliability of Bus Network,U491.17
  18. The Study on Methods of RNA Sceondary Structure Prediction,Q522
  19. Branching Models in Random Environments and Characteristic Numbers for Birth-Death Processes with Barriers,O211.65
  20. Some Precise Limit Theorems of Random Variables,O211
  21. Interactive Markov Chains: Theory and Applications,TP18

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Markov process
© 2012 www.DissertationTopic.Net  Mobile