Frontiers of Mathematics in China >
Moments of integral-type downward functionals for single death processes
Received date: 11 Dec 2019
Accepted date: 28 Jun 2020
Published date: 15 Aug 2020
Copyright
We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes. Meanwhile, main results are applied to more general integral-type downward functionals.
Key words: Single death process; integral-type functional; moment
Jing WANG , Yuhui ZHANG . Moments of integral-type downward functionals for single death processes[J]. Frontiers of Mathematics in China, 2020 , 15(4) : 749 -768 . DOI: 10.1007/s11464-020-0850-0
1 |
Chen M F. From Markov Chains to Non-Equilibrium Particle Systems. 2nd ed. Singapore: World Scientific, 2004
|
2 |
Gaver D P. Highway delays resulting from flow-stopping incidents. J Appl Probab 1969, 6(1): 137–153
|
3 |
Hou Z T, Guo Q F. Homogeneous Denumerable Markov Processes. Beijing: Science Press, 1978 (in Chinese); English translation, Beijing: Science Press and Springer, 1988
|
4 |
Liu Y Y, Song Y H. Integral-type functionals of first hitting times for continuous-time Markov chains. Front Math China, 2018, 13(3): 619–632
|
5 |
McNeil D R. Integral functionals of birth and death processes and related limiting distributions. Ann Math Statist, 1970, 41(2): 480–485
|
6 |
Moran P A P. The Theory of Storage . London: Methuen, 1959
|
7 |
Naddor E. Inventory Systems. New York: Wiley, 1966
|
8 |
Puri P S. On the homogeneous birth-and-death process and its integral. Biometrika, 1966, 53(1-2): 61–71
|
9 |
Puri P S. Some limit theorems on branching processes and certain related processes. Sankhya, 1969, 31(1): 57–74
|
10 |
Puri P S. A method for studying the integral functionals of stochastic processes with applications: I. Markov chain case. J Appl Probab, 1971, 8(2): 331–343
|
11 |
Wang J, Zhang Y H. Integral-type functional downward of single death processes. Chinese J Appl Probab Statist, 2020 (to appear, in Chinese)
|
12 |
Wang Z K. On distributions of functionals of birth and death processes and their applications in the theory of queues. Scientia Sinica, 1961, X(2): 160–170
|
13 |
Wang Z K. Distribution of first hitting time and stay time of birth and death processes. Sci China Math, 1980, 2: 13–21 (in Chinese)
|
14 |
Wang Z K. The General Theory of Stochastic Processes, Vol 2. Beijing: Beijing Normal Univ Press, 2010 (in Chinese)
|
15 |
Wu L D. Distribution of integral functional of homogeneous denumerable Markov processes. Acta Math Sinica, 1963, 13(1): 86–93 (in Chinese)
|
16 |
Yang C Q. Integral functional of denumerable Markov processes and boundary property of bilateral birth and death processes. Progress in Math, 1964, 7(4): 397–424 (in Chinese)
|
17 |
Zhang J K. On the generalized birth and death processes (I){the numeral introduction, the functional of integral type and the distributions of runs and passage times. Acta Math Sci, 1984, 4(2): 191–209
|
18 |
Zhang J K. On the generalized birth and death processes (II){the stay time, limit theorem and ergodic property. Acta Math Sci, 1986, 6(1): 1–13
|
19 |
Zhang Y H. Criteria on ergodicity and strong ergodicity of single death processes. Front Math China, 2018, 13(5): 1215{1243
|
20 |
Zhang Y H, Zhou X F. High order moments of first hitting times for single death processes. Front Math China, 2019, 14(5): 1037–1061
|
/
〈 | 〉 |