Weak geometric p-rough path
= Weak geometric p-rough path
{title2=$\mathbf X:[0,T]\to G^{\lfloor p\rfloor}(\mathbb R^d)$}
A weak geometric $p$-rough path is a continuous path in the <free step-N nilpotent Lie group>, with $N=\lfloor p\rfloor$, whose increments have finite $p$-variation for the <Carnot-Carathéodory distance>. Its multiplicative increments are $\mathbf X_{s,t}=\mathbf X_s^{-1}\otimes\mathbf X_t$. They obey the <Chen identity> and the algebraic symmetries of <path signatures>.