14 citations · 68 across the 25 of their papers we have counts for
6 papers · 1 filter
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}…
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…
On a generalisation of the Banach indicatrix theorem
Rafał M. Łochowski
We prove that for any regulated function and the infimum of the total variations of functions approximating with accuracy $c…
A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality
Rafał M. Łochowski
Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain a…
The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition
R. Ghomrasni, R. Łochowski
The play operator minimalizes the total variation on intervals , of functions approximating uniformly given regulated function with given accuracy and starting from a…
On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg Functions
Rafał M. Łochowski
For a real càdlàg function f and a positive constant c we find another càdlàg function, which has the smallest total variation pos- sible among all functions uniformly approximatin…