scholarly journals The central limit theorem for additive functionals of Markov processes and the weak convergence to Wiener measure

1970 ◽  
Vol 22 (4) ◽  
pp. 551-566 ◽  
Author(s):  
Masuyuki HITSUDA ◽  
Akinobu SHIMIZU
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
Central Limit ◽  
Markov Processes ◽  
Wiener Measure ◽  
Additive Functionals ◽  
The Central Limit Theorem

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

1967 ◽  
Vol 30 ◽  
pp. 47-56 ◽  
Author(s):  
Masatoshi Fukushima ◽  
Masuyuki Hitsuda
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
State Space ◽  
Central Limit ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Function ◽  
Time Parameter ◽  
The Central Limit Theorem

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 functionFij(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).

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