Talk:Kolmogorov equations (continuous-time Markov chains)

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What is $A_{ij}$ ?

what the heck is $A_{ij}$? Two pathetic articles- both this one and the one not containing any equation, — Preceding unsigned comment added by 83.26.215.99 (talk) 16:25, 26 May 2014 (UTC)[reply]

A_{ij}

is the transition rate matrix or generator matrix --kupirijo (talk) 06:06, 3 January 2020 (UTC)[reply]

Please define the notation

In its present state this page is pretty much useless, because it doesn't define any of its terms. It introduces P(x,s;y,t) without explaining the semicolon (is this an element of a joint distribution or a conditional one?), then states the equations in terms of $P_{ij}(s,t)$, which isn't defined either - is it the same? The matrix A is not explained either. If someone who is familiar with the subject could simply edit in brief explanations of the symbols it would make the page a lot more useful. — Preceding unsigned comment added by 157.82.34.155 (talk) 09:42, 10 July 2014 (UTC)[reply]

From what I understand the semicolon notation is a conditional probability distribution notation, i.e.

P_{ij}(s;t)

is equivalent to

\Pr(X(t)=j\mid X(s)=i)

--kupirijo (talk) 18:03, 4 January 2020 (UTC)[reply]

Merge proposal

This page and Kolmogorov equations look almost like two halves of the same page. They talk about the same concept and the introduction section reads the same. They cover different aspects of the same topic.

I propose to merge this page into Kolmogorov equations. pony in a strange land (talk) 16:25, 24 May 2023 (UTC)[reply]

Support A merger of these two makes sense to me--same topic, different aspects, and neither article so large that a merge is unreasonable. --{{u|Mark viking}} {Talk} 10:45, 25 May 2023 (UTC)[reply]

Yeah, a merge seems good. Closed Limelike Curves (talk) 20:43, 30 September 2023 (UTC)[reply]

Merger complete. Klbrain (talk) 12:14, 21 December 2023 (UTC)[reply]

Is "Master equation" a synonym of Kolmogorov equation?

After having a look at both definitions they look almost similar but the Master equations are differential equations of the probabilities to be a state at a time t, and the Kolmogorov equations are differential equations of the transition probabilities at a time t. This could be a mistake, but if someone could confirm we should edit the page to make it less confusing. 176.173.221.165 (talk) 17:51, 12 December 2023 (UTC)[reply]

What is A i j {\displaystyle A_{ij}} ?

Please define the notation

Merge proposal

Is "Master equation" a synonym of Kolmogorov equation?

What is $A_{ij}$ ?