scholarly journals Zero-sum risk-sensitive stochastic games on a countable state space

2014 ◽  
Vol 124 (1) ◽  
pp. 961-983 ◽  
Author(s):  
Arnab Basu ◽  
Mrinal Kanti Ghosh
Keyword(s):  
State Space ◽  
Stochastic Games ◽  
Countable State Space ◽  
Risk Sensitive ◽  
Countable State ◽  
Zero Sum

scholarly journals Characterization and simplification of optimal strategies in positive stochastic games

2018 ◽  
Vol 55 (3) ◽  
pp. 728-741 ◽  
Author(s):  
János Flesch ◽  
Arkadi Predtetchinski ◽  
William Sudderth
Keyword(s):  
State Space ◽  
Optimal Strategy ◽  
Stochastic Games ◽  
Optimal Strategies ◽  
Action Space ◽  
Positive Zero ◽  
Countable State ◽  
Zero Sum ◽  
Action Spaces

Abstract We consider positive zero-sum stochastic games with countable state and action spaces. For each player, we provide a characterization of those strategies that are optimal in every subgame. These characterizations are used to prove two simplification results. We show that if player 2 has an optimal strategy then he/she also has a stationary optimal strategy, and prove the same for player 1 under the assumption that the state space and player 2's action space are finite.

THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT

2017 ◽  
Vol 32 (4) ◽  
pp. 626-639 ◽  
Author(s):  
Zhiyan Shi ◽  
Pingping Zhong ◽  
Yan Fan
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Random Environment ◽  
Cayley Tree ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Countable State Space ◽  
Large Numbers ◽  
Countable State ◽  
Definition Of

In this paper, we give the definition of tree-indexed Markov chains in random environment with countable state space, and then study the realization of Markov chain indexed by a tree in random environment. Finally, we prove the strong law of large numbers and Shannon–McMillan theorem for Markov chains indexed by a Cayley tree in a Markovian environment with countable state space.

Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol

1987 ◽  
Vol 24 (02) ◽  
pp. 347-354 ◽  
Author(s):  
Guy Fayolle ◽  
Rudolph Iasnogorodski
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
Stochastic Processes ◽  
State Space ◽  
Discrete Time ◽  
Random Variables ◽  
Countable State Space ◽  
Countable State ◽  
New Criteria

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn ), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn ) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.

scholarly journals Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 253 ◽  
Author(s):  
Alexander Zeifman ◽  
Victor Korolev ◽  
Yacov Satin
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Continuous Time ◽  
Countable State Space ◽  
Perturbation Bounds ◽  
Queuing Models ◽  
Continuous Time Markov Chains ◽  
Quantitative Estimates ◽  
Countable State

This paper is largely a review. It considers two main methods used to study stability and to obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible “perturbed” processes are calculated.

Kolmogorov's differential equations for non-stationary, countable state Markov processes with uniformly continuous transition probabilities

1973 ◽  
Vol 73 (1) ◽  
pp. 119-138 ◽  
Author(s):  
Gerald S. Goodman ◽  
S. Johansen
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
State Space ◽  
Markov Processes ◽  
Transition Probabilities ◽  
The State ◽  
Continuous Transition ◽  
Countable State Space ◽  
Countable State ◽  
Uniformly Continuous

1. SummaryWe shall consider a non-stationary Markov chain on a countable state space E. The transition probabilities {P(s, t), 0 ≤ s ≤ t <t0 ≤ ∞} are assumed to be continuous in (s, t) uniformly in the state i ε E.

Sign in / Sign up

Export Citation Format

Share Document