= Orthogonal continuous local martingales
{title2=$[M,N]=0$}
Two <continuous local martingales> are orthogonal when their <quadratic covariation> is zero. With zero initial values, the <martingale product identity> says that their product is a <local martingale>. For two <Brownian motions> in a common <filtration>, orthogonality and the <Lévy characterization of multidimensional Brownian motion> make the pair a two-dimensional <Brownian motion> and imply independence. Merely having the two marginal <Brownian motion> laws on the same space does not imply orthogonality.
Back to article page
