Lévy area
= Lévy area
{c}
{title2=$A^{ij}_{s,t}=\tfrac12\int_s^t((B^i_r-B^i_s)\circ dB^j_r-(B^j_r-B^j_s)\circ dB^i_r)$}
Lévy area is the antisymmetric second-level integral of multidimensional <Brownian motion>. For distinct independent components the integrals are also <Itô integrals>. Combined with the symmetric tensor $\tfrac12 B_{s,t}^{\otimes2}$, it gives the second level of <enhanced Brownian motion>. It is not continuously determined by the uniform norm of the Brownian path.