Optimal Extension to Sobolev Rough Paths
Optimal Extension to Sobolev Rough Paths
Abstract We show that every $\mathbb {R}^{d}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>ℝ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> </mml:msup> </mml:math> -valued Sobolev path with regularity α and integrability p can be lifted to a weakly geometric rough path in the sense of T. Lyons with exactly the same regularity and integrability, provided …