Related papers: Measuring the roughness of random paths by increme…
Surface roughness is primary measure of pavement performance that has been associated with ride quality and vehicle operating costs. Of all the surface roughness indicators, the International Roughness Index (IRI) is the most widely used.…
Optimal sample path properties of stochastic processes often involve generalized H\"{o}lder- or variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of $\psi (x) \equiv $…
A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a…
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for…
Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to H\"older continuous multiplicative functionals in the case of Lipschitz coefficients…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each…
The It\^o formula, also known as the change-of-variables formula, is a cornerstone of It\^o stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. Since…
The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. We study the asymptotic behavior of the raking-ratio empirical process…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
In tribology, it is of importance to properly characterize the topography of rough surfaces. In this work, the three-dimensional topographies of plain grinding surfaces are measured through a white light interferometer, and their…
We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…
We estimate the Hurst parameter $H \in (0,1)$ of a fractional Brownian motion from discrete noisy data, observed along a high frequency sampling scheme. When the intensity $\tau_n$ of the noise is smaller in order than $n^{-H}$ we establish…
Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities.…
Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…