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ynotidas
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how do i show that a markov chain is irreducible?
How do i show that a markov chain is irreducible?
- Context: Undergrad
- Thread starter ynotidas
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- Chain Markov chain
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SUMMARY
To demonstrate that a Markov chain is irreducible, one must establish that for every pair of states (r, s), there exists an integer t such that the transition probability p[r, s, t] is greater than 0. This means that it is possible to reach state s from state r in a finite number of steps. The concept of irreducibility is crucial in the study of Markov chains, as it ensures that all states communicate with each other.
PREREQUISITES- Understanding of Markov chains and their properties
- Familiarity with transition probabilities
- Knowledge of finite state spaces
- Basic concepts of stochastic processes
- Study the concept of transition matrices in Markov chains
- Learn about the classification of states in Markov chains
- Explore the concept of aperiodicity in Markov chains
- Investigate the implications of irreducibility on long-term behavior of Markov chains
Mathematicians, statisticians, data scientists, and anyone studying stochastic processes or working with Markov chains in various applications.
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