Let W be a Wiener process. For r> 0 and T> 0 let IW (T, r) 2 denote the minimal value of the
energy∫ 0 T h′(t) 2 dt taken among all absolutely continuous functions h (⋅) defined on [0 …

We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener
process and a random walk. Under certain assumptions on the band width, it is shown that …

The play operator minimalizes the total variation on intervals,[0, T], T> 0, of functions
approximating uniformly given regulated function with given accuracy and starting from a …

Using a new technique, based on the regularisation of a càdlàg process via the double
Skorohod map, we obtain limit theorems for integrated numbers of level crossings of …

For any real-valued stochastic process X with càdlàg paths we define non-empty family of
processes which have locally finite total variation, have jumps of the same order as the …

For a real càdlàg path x, we define sequence of semi-explicit quantities, which do not
depend on any partitions and such that whenever x is a path of a càdlàg semimartingale …

In the article, we find the asymptotic distribution of the derivative of the taut string
accompanying a Wiener process in a strip of fixed width on long time intervals. This enables …

For a real càdlàg function f defined on a compact interval, its truncated variation at the level
c>0 is the infimum of total variations of functions uniformly approximating f with accuracy c/2 …

We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly
restricted downward jumps possess quadratic variation, which does not depend on the …

[1508.01269] Asymptotics of the truncated variation of model-free price paths and
semimartingales with jumps close this message arxiv Smilely Bones Happy Open Access Week …