Related papers: Forecasting of time data with using fractional Bro…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
In this paper, we investigate a deep learning method for predicting path-dependent processes based on discretely observed historical information. This method is implemented by considering the prediction as a nonparametric regression and…
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…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…
Recent advances in time series, where deterministic and stochastic modelings as well as the storage and analysis of big data are useless, permit a new approach to short-term traffic flow forecasting and to its reliability, i.e., to the…
The $d$-dimensional fractional Brownian motion (FBM for short) $B_t=((B_t^{(1)},...,B_t^{(d)}),t\in\mathbb{R})$ with Hurst exponent $\alpha$, $\alpha\in(0,1)$, is a $d$-dimensional centered, self-similar Gaussian process with covariance…
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…
We consider the time discretization of fractional stochastic wave equation with Gaussian noise, which is negatively correlated. Major obstacles to design and analyze time discretization of stochastic wave equation come from the…
In this paper it is reconsidered the prediction problem in time series framework by using a new non-parametric approach. Through this reconsideration, the prediction is obtained by a weighted sum of past observed data. These weights are…
We propose a statistical space-time model for predicting atmospheric wind speed based on deterministic numerical weather predictions and historical measurements. We consider a Gaussian multivariate space-time framework that combines…
In the last two decades, a number of methods have been proposed for forecasting based on fuzzy time series. Most of the fuzzy time series methods are presented for forecasting of car road accidents. However, the forecasting accuracy rates…
In this article, we present the least squares estimator for the drift parameter in a linear regression model driven by the increment of a fractional Brownian motion sampled at random times. For two different random times, Jittered and…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
We extend the theoretical results for any FOU(p) processes for the case in which the Hurst parameter is less than 1/2 and we show theoretically and by simulations that under some conditions on T and the sample size n it is possible to…
This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.