Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)

Phumlani L. Zondi, Darlington Hove, Rafał M. Łochowski +1

We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}…