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math.CA2025
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}…
math.CA2024
Local times of deterministic paths with finite variation
Darlington Hove, Farai J. Mhlanga, Rafał M. Łochowski +1
In this note, we define the numbers of level crossings by a c{à}dl{à}g (RCLL) real function and, in analogy to the work of Bertoin and Yor [BY14] we…