Related papers: The effect of round-off error on long memory proce…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…
We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…
This paper develops the asymptotic theory for parametric and nonparametric regression models when the errors have a fractional local to unity root (FLUR) model structure. FLUR models are stationary time series with semi-long range…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy…
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov…
We propose a new discrete-time online parameter estimation algorithm that combines two different aspects, one that adds momentum, and another that includes a time-varying learning rate. It is well known that recursive least squares based…
We present new mechanisms for \emph{label differential privacy}, a relaxation of differentially private machine learning that only protects the privacy of the labels in the training set. Our mechanisms cluster the examples in the training…
We develop a novel a posteriori error estimator for the $L^2$ error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization…
In this paper, the weak convergence about the discretization error of stochastic iterated integrals in the Skorohod sense are studied, while the integrands and integrators of iterated integrals are supposed to be semimartingales with jumps.…
We present a family of generalized Hessian estimators of the objective using random direction stochastic approximation (RDSA) by utilizing only noisy function measurements. The form of each estimator and the order of the bias depend on the…
We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
In this work, the motion of a dust particle under the influence of the random force due to dust charge fluctuations is considered as a non-Markovian stochastic process. Memory effects in the velocity process of the dust particle are…
A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their…
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…
The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by microscopy techniques. In this study, we present a…
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
In this paper, by comparing the time scales associated with the velocity relaxation and correlation time of the random force due to dust charge fluctuations, memory effects in the velocity relaxation of an isolated dust particle exposed to…
We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples…