
The Qualitative Theory for Birth and Death Processes with Barrier
Xiang Qun YANG, Lin XIAO, He Song WANG
Acta Mathematica Sinica, Chinese Series ›› 2010, Vol. 53 ›› Issue (5) : 1019-1026.
The Qualitative Theory for Birth and Death Processes with Barrier
birth and death process with barrier / qualitative theory / kinds of barrier {{custom_keyword}} /
[1] Wang Z. K., Yang X. Q., The Birth and Death Processes and Markov Chains, Beijing: Science Press (Second Edition), 2005 (in Chinese); Berlin: Springer and Beijing: Science Press, 1992 (in English).
[2] Anderson W. J., Continuous-Time Markov Chains, Berlin: Springer, 1991.
[3] Yang X. Q., The Construction Theory of Denumerable Markov Processes, Changsha: Hunan Science and Technology Press (Second Edition), 1986 (in Chinese); Chicheser UK: Wiley and Sons, 1990 (in English).
[4] Revuz D., Markov Chains, Amsterdam: North Holland, 1984.
[5] Shao J. H., Mao Y. H., Estimation of the Dirichlet eigenvalues of Birth-Death process on Trees, Acta Mathematica Sinica, Chinese Series, 2007, 50(3): 507--516.
[6] Chen M. F., Variational formulas of poincar ê-type Inequalities for Birth-Death Processes, Acta Mathematica Sinica, English Series, 2003, 19(4): 625--644.
[7] Zhu Q. X., Dai Y. L., Properties of the Birth and Death Processes with Zero as Their Leap-reflecting Barriers before Explosion, Acta Mathematica Scientia, 2007, 27A(3): 456--469 (in Chinese).
[8] Zhu Q. X., Yang X. Q., Downward Properties of the Birth and Death Processes with Zero as their Reflecting and Quasi-leap-reflecting Barriers before Explosion, Chinese Journal of Applied Probability and Statistics, 2005, 21(2): 188--196 (in Chinese).
[9] Zhu Q. X., Shu X. B., Characteristic numbers and their probability meaning of two kinds of birth and death processes, Applied Mathematics A Journal of Chinese Universities, 2006, 21A(3): 311--320 (in Chinese).
[10] Feller W., The Birth and Death processes as diffusion processes, J. Math. Pures Appl., 1959, 9: 301--345.
[11] Yang X. Q., A class of birth and death processes, Acta Math., 1965, 15: 9--31 (in Chinese); Chinese Mathematics, translation of Acta Mathematica Sinica, New Series, 1965, 6: 305--329.
[12] Wang Z. K., The construction theory of birth and death processes, Chin. Math. Adv., 1962, 5: 137--187 (in Chinese).
[13] Wang Z. K., Yang X. Q., The construction for stopping birth and death processes, Acta Mathematica Sinica, Chinese Series, 1978, 21: 61--71.
[14] Yang X. Q., Wang Z. K., Probability-Analysis method in construction theory for stopping birth and death processes, J. Nankai Univ. (Natural Sci.), 1979, 3: 1--32 (in Chinese).
[15] Yang X. Q., Note on the construction theory of birth and death processes, Acta Mathematica Sinica, Chinese Series, 1965, 15(1): 173--187; Chinese Mathematica, translation of Acta Mathematica Sinica, New Series, 1965, 6: 479--494.
[16] Gao P., The birth and death processes with zero as their absorbing barrier, Acta Math. Appl. Sinica, 1985, 2(4): 292--303.
[17] Yang X. Q., Distribution of lifetime after explosion for birth and death processes, Science in China, Ser A, 1998, 41(7): 694--699.
[18] Yang X. Q., Some properties of repeated hits after first explosion for birth and death processes, Science in China, Ser A, 1992, 42(5): 471--477.
[19] Yang X. Q., Liu S. Y., Joint distribution of first hitting time and first hitting location after explosion for birth and death processes, Science in China, Ser A, 2000, 43(1): 1014--1018.
[20] Yang X. Q., Liu S. Y., Decomposition and embedment of trajectory after explosion for a birth and death processes, Science in China, Ser A, 2002, 45(1): 1100--1105.
[21] Yang X. Q., Wang H. S,, Unified characteristic numbers and solution of equations for birth and death processes with barrier, Acta Mathematica Sinica, English Series, Accepted.
/
〈 |
|
〉 |