Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On limit distributions of normalized truncated variation, upward
  truncated variation and downward truncated variation processes   In the paper we introduce the truncated variation, upward truncated variation
and downward truncated variation. These are closely related to the total
variation but are well-defined even if the latter is infinite. Our aim is to
explore their feasibility to studies of stochastic processes. We concentrate on
a Brownian motion with drift for which we prove the convergence of the above-
mentioned quantities. For example, we study the truncated variation when the
truncation parameter c tends to 0. We prove in this case that for "small" c's
it is well-approximated by a deterministic process. Moreover we prove that
error in this approximation converges weakly (in functional sense) to a
Brownian motion. We prove also similar result for truncated variation processes
when time parameter is rescaled to infinity. We stress that our methodology is
robust. A key to the proofs was a decomposition of the truncated variation (see
Lemmas 11 and 12). It can be used for studies of any continuous processes. Some
additional results like an analog of the Anscombe-Donsker theorem and the
Laplace transform of time to given drawdown by c (and analogously drawup till
time) are presented.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph