Markov Chains¶
Norris, J. R. (1997). Markov Chains. Cambridge University Press.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Markov Process
- The structural claim is sharp and almost paradoxically strong: a single, sufficiently-rich present state is a complete summary of all history relevant to the future, so prediction requires only the state now and a transition rule, not the trajectory that produced it.
This sourceCanonical modern textbook: develops the Markov property as a conditional-independence statement (present state screens off the past), the state–transition-kernel structure, sufficient-statistic framing, and long-run behavior (stationary distributions, mixing, recurrence/absorption) determined by the transition structure alone.
- The structural claim is sharp and almost paradoxically strong: a single, sufficiently-rich present state is a complete summary of all history relevant to the future, so prediction requires only the state now and a transition rule, not the trajectory that produced it.
- Stochastic Process
- The Markov toolkit — transition kernels, stationary distributions, mixing times, absorbing-state analysis — transfers from statistical physics (the Metropolis dynamics) to NLP (hidden Markov models) to operations (queue occupancy) to PageRank, because all are Markov processes and the present-screens-off-the-past structure licenses the same eigenvalue and steady-state machinery.
This sourceDevelops transition kernels, stationary distributions, mixing, and absorbing-state analysis for the Markov subclass of stochastic processes.
- The Markov toolkit — transition kernels, stationary distributions, mixing times, absorbing-state analysis — transfers from statistical physics (the Metropolis dynamics) to NLP (hidden Markov models) to operations (queue occupancy) to PageRank, because all are Markov processes and the present-screens-off-the-past structure licenses the same eigenvalue and steady-state machinery.
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