AM  Vol.5 No.21 , December 2014
Orbital Properties of Regular Chain
ABSTRACT
The strong Markov process had been obtained by Ray-Knight compacting; its orbit natures are discussed; the significance probability of kolmogorov forward and backward equations are explained.

Cite this paper
Zhang, K. , Du, H. , Meng, H. and Ba, M. (2014) Orbital Properties of Regular Chain. Applied Mathematics, 5, 3311-3317. doi: 10.4236/am.2014.521308.
References
[1]   Rockner, M. and Wang, F.Y. (2004) Weak Poincare Inequalities and L2-Convergence Rates of Markov Semi-Groups. Journal of Functional Analysis, 185, 564-603.
http://dx.doi.org/10.1006/jfan.2001.3776

[2]   Xie, F.Y., Wu, B. and Hu, Y.M. (2013) A Generalized Markov Chain Model Based on Generalized Interval Probability. Science China Technological Sciences, 56, 2132-2136.
http://dx.doi.org/10.1007/s11431-013-5285-3

[3]   Dong, J.C. (2006) Ray-Knight Compactification of Markov Chain. Ph.D., Zhengzhou University, Zengzhou.

[4]   Xiao, Y.M. (2014) Criterion of Semi-Markov Dependent Risk Model. Acta Mathematica Sinica (English Series), 30, 1273-1280.
http://dx.doi.org/10.1007/s10114-014-3249-6

[5]   Barthe, F., Cattiaux, P. and Roberto, C. (2007) Isoperimetry between Exponential and Gaussian. Electronic Journal of Probability, 12, 1212-1237.
http://dx.doi.org/10.1214/EJP.v12-441

[6]   Barthe, F., Cattiaux, P. and Roberto, C. (2006) Interpolated Inequalities between Exponential and Gaussian, Orlicz Hyper Contractivity and Isoperimetry. Revista Matemática Iberoamericana, 22, 993-1066.
http://dx.doi.org/10.4171/RMI/482

[7]   Chen, L. (2012) Paths of Bilateral Birtth-Death Processes and Construction Theory(I). Journal of Henan University (Nature Science), 42, 337-342.

[8]   Zhang, L.C. and Guo, M.Z. (2014) The Characterization of a Class of Quantum Markov Semi-Groups and the Associated Operator-Valued Dirichlet Forms Based on Hilbert C*-Module l2(A). Science China Mathematics, 57, 377-387.
http://dx.doi.org/10.1007/s11425-013-4678-x

[9]   Chen, L. (2013) Paths of Bilateral Birth-Death Processes and Construction Theory(II). Journal of Henan University (Nature Sciencd), 43, 5-10.

[10]   Zou, B., Xu, Z.B. and Xu, J. (2014) Generalization Bounds of ERM Algorithm with Markov Chain Samples. Acta Mathematicae Applicatae Sinica (English Series), 30, 223-238.
http://dx.doi.org/10.1007/s10255-011-0096-4

[11]   Shimomura, H. (1994) Poisson Measures on Configuration Space and Unitary Representation of the Group of Diffeomorphisms. Journal of Mathematics of Kyoto University, 34, 599-614.

[12]   Xu, C.W. and Yan, G.J. (2011) Martin Entrance Boundary and Ray-Knight Compactification of Minimal Q-Processes. Chinese Journal of Applied Probability and Statistics, 27, 633-641.

[13]   Yang, W.J. (2014) Some Researches of Strong Limit Theorems for Markov Chains Indexed by Trees. Advances in Mathematics (China), 32, 206-218.

[14]   Wen, S.F., Xu, M. and Wang, F.L. (2014) A New Method to Estimate Markov State Transition Probability Matrix. Mathematics in Practice and Theory, 44, 164-168.

[15]   Wang, Z.K. (2005) Birth-Death Processes and Markov Chain. Science Press, Beijing.

[16]   Xiang, X.Y. (2013) The Q-Matrix of Ring Markov Chain. ACTA Mathematica Sinica (Chinese Series), 56, 735-750.

[17]   Luckock, H. (2003) A Steady-State Model of the Continuous Double Auction. Quantitative Finance, 3, 385-404.
http://dx.doi.org/10.1088/1469-7688/3/5/305

 
 
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