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What is the best way to denote,

Probability of $n_i$ changing its value from $0$ to $1$ at time $t$. I come up with these, any suggestions _

$$ P_{n_i,0\rightarrow1}(t) \\ P(n_i:0\rightarrow1, t) $$

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If you define the notation, you can use it. – Hagen von Eitzen Feb 20 '13 at 12:32
Another option might be $P_0^1(n_i,t)$, or in general $P_x^y(n_i,t)$ for "Probability of $n_i$ changing from $x$ to $y$ at time $t$". – icurays1 Feb 20 '13 at 14:57
I am not sure that's what you mean but : $$P(n_i(t)=1 | n_i(0) = 0)$$ – Inquest Feb 20 '13 at 14:58
It depends on the wider context, e.g. which other transitions are possible? For instance, if transitions are always only to the successor, you don't need to mention both the source and the destination. There's also a question where your focus is: Are you mostly considering these as functions of $t$, or of $i$, or of $n_i$? If $t$ is more like a parameter, you might want to write it as a subscript. – joriki Feb 20 '13 at 15:07
$n_i$ is most important. – NoviceEuler Feb 21 '13 at 8:51

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