Martingale difference sequence
= Martingale difference sequence
{title2=$\mathbb E[D_n\mid\mathcal F_{n-1}]=0$}
A martingale difference sequence is an <adapted> sequence of integrable random variables $D_n$, $n\geq1$, with $\mathbb E[D_n\mid\mathcal F_{n-1}]=0$. Its partial sums are a <martingale>, and martingale increments give such sequences. If the differences are square-integrable, they are <uncorrelated random variables>: for $j<k$, conditioning on $\mathcal F_{k-1}$ gives $\mathbb E D_jD_k=0$.