Feb 24, 2026 · I am analyzing a discrete-time Markov chain that can grow exponentially but also suffers from frequent, severe drops. I want to find the exact probability that it reaches a certain threshold …

Apr 25, 2017 · A Markov process is basically a stochastic process in which the past history of the process is irrelevant if you know the current system state. In other words, all information about the …

Mar 11, 2015 · Markov's Inequality and its corollary Chebyshev's Inequality are extremely important in a wide variety of theoretical proofs, especially limit theorems. A previous answer provides an example.

I would like to know what books people currently like in Markov Chains (with syllabus comprising discrete MC, stationary distributions, etc.), that contain many good exercises. Some such book on

Jul 22, 2025 · For irreducible Markov chains, if a state is recurrent, then every other state in the state space is automatically recurrent as well. This holds analogously for positive recurrence and null …

Jul 23, 2010 · 7 Markov chains, especially hidden Markov models are hugely important in computation linguistics. A hidden Markov model is one where we can't directly view the state, but we do have …

Note that this version of the Riesz-Markov-Kakutani theorem is much stronger than the usually stated one, which is concerned positive functionals on $\mathbb {R}$. The fact that the dual norm is the …

Apr 28, 2022 · 0 Imagine the following Markov chain: $$\begin {bmatrix} 0 & 0.5 & 0.5 \\ 1 & 0 & 0 \\ 1 & 0 & 0\end {bmatrix}$$ We always get back to state 1 in two time periods. So, state 1 is periodic and …

Aug 23, 2015 · Finally, note that n-grams, for instance, illustrate a canonical example of the distinction above between Markov processes and the simplest possible memoryless processes.

Markov processes and, consequently, Markov chains are both examples of stochastic processes. Random process and stochastic process are completely interchangeable (at least in many books on …