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On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem

Published online by Cambridge University Press:  22 January 2016

Masatoshi Fukushima  and
Masuyuki Hitsuda
Masatoshi Fukushima
Affiliation:
Tokyo University of Education and Nagoya University
Masuyuki Hitsuda
Affiliation:
Tokyo University of Education and Nagoya University
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We shall consider a class of Markov processes (n(t), x(t)) with the continuous time parameter t∈e[0, ∞), whose state space is {1, 2,..., N}×R1. We shall assume that the processes are spacially homogeneous with respect to X∈R1. In detail, our assumption is that the transition function

Fij(x,t) = P(n(t) = j, x(t)≦x|n(0) = i,x(0) = 0), t > 0, 1≦i, j,≦N, x∈R1satisfies following conditions (1, 1)~(1,4).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 47 - 56
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Gnedenko, B.V. and Kolmogorov, A.N.: Limit distributions for sums of independent random variables, Addison-Wesley Pub. Comp., (1954), (Translated from the Russian.)Google Scholar
[2] Harris, T.E.: The theory of branching processes, Springer-Verlag, (1963).Google Scholar
[3] Keilson, J. and Wishart, D.M.G.: A central limit theorem for processes detined on a finite Markov chain, Proc. Camb. Phil. Soc, 60 (1964), 547–567.CrossRefGoogle Scholar
[4] Feller, W.: An introduction to probability theory and its application vol. 2, John Wiley & Sons, (1966).Google Scholar