The central limit theorem for additive functionals of Markov and semi-Markov processes

1987 ◽  
Vol 38 (5) ◽  
pp. 2299-2308 ◽  
Author(s):  
V. S. Korolyuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Processes ◽  
Additive Functionals ◽  
The Central Limit Theorem ◽  
Semi Markov Processes

scholarly journals Finite-memory elephant random walk and the central limit theorem for additive functionals

2021 ◽  
Vol 35 (2) ◽  
Author(s):  
Iddo Ben-Ari ◽  
Jonah Green ◽  
Taylor Meredith ◽  
Hugo Panzo ◽  
Xioran Tan
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Additive Functionals ◽  
The Central Limit Theorem ◽  
Finite Memory

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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