A note on entrywise perturbation theory for Markov chains
โ Scribed by Jungong Xue
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 172 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
โฆ Synopsis
O'Cinneide presented an entrywise perturbation theorem for Markov chains. The error bound he obtained is nearly best possible. We give the best possible error bound.
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Using the electric network approach, we give closed-form formulas for the stationary probabilities and expected hitting times in balanced circular Markov chains. As an application, we give a closed-form formula for the duration of play in the general ruin problem, where the probabilities of winning
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