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math.PR2011★ 11 cited
On truncated variation, upward truncated variation and downward truncated variation for diffusions
Rafał M. Łochowski, Piotr Miłoś
The truncated variation, , is a fairly new concept introduced in [5]. Roughly speaking, given a càdlàg function , its truncated variation is "the total variation which doe…
math.PR2011★ 1 cited
On Pathwise Uniform Approximation of Processes with Càdlàg Trajectories by Processes with Minimal Total Variation
Rafał M. Łochowski
For a real cadlag function and positive constant we find another cadlag function, which has the smallest total variation possible among the functions uniformly approximatin…
math.PR2011
On pathwise uniform approximation of processes with càdlàg trajectories by processes with finite total variation
Rafał M. Łochowski
For any real-valued stochastic process X with càdlàg paths we define non-empty family of processes, which have finite total variation, have jumps of the same order as the process X…