Content deleted Content added
m Task 18 (cosmetic): eval 8 templates: del empty params (4×); hyphenate params (5×); |
|||
Line 142:
As ''n'' was arbitrary, this reasoning holds for any ''n'', and therefore for reversible Markov chains '''{{pi}}''' is always a steady-state distribution of Pr(''X''<sub>''n''+1</sub> = ''j'' | ''X''<sub>''n''</sub> = ''i'') for every ''n''.
If the Markov chain begins in the steady-state distribution, that is, if <math>\Pr(X_0=i)=\pi_i</math>, then <math>\Pr(X_n=i)=\pi_i</math> for all <math>n</math> and the detailed balance equation can be written as
:<math>\Pr(X_{n} = i, X_{n+1} = j) = \Pr(X_{n+1} = i, X_{n} = j)\,.</math>
| |||