N—Person Stochastic Games: Extensions of the Finite State Space Case and Correlation

2003 ◽  
pp. 93-106 ◽  
Author(s):  
Andrzej S. Nowak
Keyword(s):  
State Space ◽  
Stochastic Games ◽  
Finite State ◽  
Space Case ◽  
Finite State Space

scholarly journals The combinational structure of non-homogeneous Markov chains with countable states

1983 ◽  
Vol 6 (2) ◽  
pp. 371-385
Author(s):  
A. Mukherjea ◽  
A. Nakassis
Keyword(s):  
State Space ◽  
Countable State Space ◽  
Continuous Parameter ◽  
Homogeneity Condition ◽  
Weak Homogeneity ◽  
Countable Product ◽  
Countable State ◽  
Finite State ◽  
Space Case ◽  
Finite State Space

LetP(s,t)denote a non-homogeneous continuous parameter Markov chain with countable state spaceEand parameter space[a,b],−∞<a<b<∞. LetR(s,t)={(i,j):Pij(s,t)>0}. It is shown in this paper thatR(s,t)is reflexive, transitive, and independent of(s,t),s<t, if a certain weak homogeneity condition holds. It is also shown that the relationR(s,t), unlike in the finite state space case, cannot be expressed even as an infinite (countable) product of reflexive transitive relations for certain non-homogeneous chains in the case whenEis infinite.

Rate modulation in dams and ruin problems

1996 ◽  
Vol 33 (2) ◽  
pp. 523-535 ◽  
Author(s):  
Søren Asmussen ◽  
Offer Kella
Keyword(s):  
State Space ◽  
Release Rate ◽  
Risk Process ◽  
The State ◽  
Limiting Distribution ◽  
Process Conditions ◽  
Explicit Formulas ◽  
Rate Modulation ◽  
Finite State ◽  
Finite State Space

We consider a dam in which the release rate depends both on the state and some modulating process. Conditions for the existence of a limiting distribution are established in terms of an associated risk process. The case where the release rate is a product of the state and the modulating process is given special attention, and in particular explicit formulas are obtained for a finite state space Markov modulation.

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