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

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

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

Please define the notation

What is $A_{ij}$ ?