Markov Chain Norris Info

She was asleep when he sat down in the plastic chair beside her. He didn’t know what to do. Markov chains didn’t cover this. There was no transition probability for how to sit with your dying daughter after eleven years of silence .

He put on his coat.

The latter half of the book moves to continuous-time Markov Chains (processes like the Poisson process or Birth-Death processes). Here, the transition matrix is replaced by a , and Norris explains the relationship between the matrix $Q$ and the transition semigroup $P(t) = e^{tQ}$.

She squeezed his hand. “The only thing that matters,” she whispered, “is the next step.” markov chain norris

One of the central goals in the Norris text is finding a probability distribution $\pi$ such that: $$\pi P = \pi$$ If the chain starts with distribution $\pi$, it remains in that distribution forever.

A Markov Chain is a mathematical system that undergoes transitions from one state to another, where the probability of transitioning from one state to another is dependent on the current state. This means that the future state of the system depends only on its current state, and not on any of its past states. This property, known as the "memoryless" property, makes Markov Chains particularly useful for modeling complex systems that exhibit random behavior.

She reached out a thin hand. He took it. Her fingers were cold. And then, for the first time in eleven years, he did something that was not in any of his textbooks: he remembered. She was asleep when he sat down in

He remembered her at age five, building towers of wooden blocks, then knocking them down with a shriek of joy. He remembered her at fourteen, crying in the kitchen because a boy had called her ugly. He remembered the last fight—the one about her mother, about his emotional absence, about the word conditional used as a weapon.

Inside was a single sheet:

He taped it to the wall above his desk. Then he opened his laptop and deleted the final chapter of his new book—the one titled The Memoryless Self . There was no transition probability for how to

On the last morning, the sun broke through the Cambridge rain. Chloe died at 7:43 a.m., with her hand in his.

The chain calculates the likelihood of each transition.

Dad, I’m in the Royal Infirmary. Ward 14. They say it’s serious. I don’t know if you’ll come. It doesn’t matter what happened before. Only what happens now. — Chloe