Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring the roughness of random paths by increment ratios   A statistic based on increment ratios (IR) and related to zero crossings of
increment sequence is defined and studied for measuring the roughness of random
paths. The main advantages of this statistic are robustness to smooth additive
and multiplicative trends and applicability to infinite variance processes. The
existence of the IR statistic limit (called the IR-roughness below) is closely
related to the existence of a tangent process. Three particular cases where the
IR-roughness exists and is explicitly computed are considered. Firstly, for a
diffusion process with smooth diffusion and drift coefficients, the
IR-roughness coincides with the IR-roughness of a Brownian motion and its
convergence rate is obtained. Secondly, the case of rough Gaussian processes is
studied in detail under general assumptions which do not require stationarity
conditions. Thirdly, the IR-roughness of a L\'evy process with $\alpha-$stable
tangent process is established and can be used to estimate the fractional
parameter $\alpha \in (0,2)$ following a central limit theorem.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph