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Horálek, Vratislav
On the moments in nonhomogeneous birth, immigration and death processes. (English). Aplikace matematiky, vol. 15 (1970), issue 1, pp. 31-40
MSC: 60-67 | MR 0256472 | Zbl 0201.21502 | DOI: 10.21136/AM.1970.103265
Summary:
Several internal relations in the form of equalities and inequalities between the first three general moments in nonhomogeneous processes: birth-death process, birth process, death process, birth-immigration-death process and immigration-death process are derived.
References:
[1] M. S. Bartlett: An Introduction to Stochastic Processes with Special Reference to Methods and Applications. Cambridge University Press 1955. MR 0068772 | Zbl 0068.11801
[2] V. Horálek: On some types of nonhomogeneous birth-immigration-death processes. Aplikace matematiky 9 (1964), 421-434. MR 0185678
[3] V. Horálek: Nonhomogeneous birth-death processes with constant ratio of rates. Aplikace matematiky 11 (1966), 296-302. MR 0214152
[4] D. G. Kendall: On the generalized birth and death process. Ann. Math. Statistics 19 (1948), 1-15. DOI 10.1214/aoms/1177730285 | MR 0024091 | Zbl 0032.17604
[5] J. E. Parzen: Stochastic Processes. Holden-Day, San Francisco, 1964, 2nd Edit. MR 0139192
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