Geometric p-rough path
= Geometric p-rough path
A geometric $p$-rough path is a limit, in the <rough path metric>, of <path signatures> of sufficiently regular paths. It is a <weak geometric p-rough path>. At the same exponent these definitions need not coincide; weak geometric paths can be approximated after slightly weakening the variation exponent. The Brownian enhancement is geometric for every $p>2$.