Related papers: Fractals with point impact in functional linear re…
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…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
Let $B=(B_1(t),\ldots,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be…
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the…
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
This paper addresses the problem of estimating the Hurst exponent of the fractional Brownian motion from continuous time noisy sample. Consistent estimation in the setup under consideration is possible only if either the length of the…
A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with…
Extending deterministic compartments pharmacokinetic models as diffusions seems not realistic on biological side because paths of these stochastic processes are not smooth enough. In order to extend one compartment intra-veinous bolus…
In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…
The practice of stochastic sensitivity analysis described in the decision analysis literature is a testimonial to the need for considering deviations from precise point estimates of uncertainty. We propose the use of Bayesian fuzzy…
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…
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…