Related papers: Parameter estimation and long-range dependence of …
We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…
On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum…
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown…
A method is described, which computes from an observed sample of events upper limits for production rates of particles, or, in case of appearance of a signal, the probability for an upwards fluctuation of the background. For any candidate,…
This paper, that will appear in the Notices of the AMS, begins with a brief historical account of the beginnings of fractional calculus and the crucial roles played by Leibniz and Fourier. Fourier's definition of fractional derivative is…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…
A notable result from analysis of Boolean functions is the Basic Invariance Principle (BIP), a quantitative nonlinear generalization of the Central Limit Theorem for multilinear polynomials. We present a generalization of the BIP for…
In this paper we study a parametric class of stochastic processes to model both fast and slow anomalous diffusion. This class, called generalized grey Brownian motion (ggBm), is made up off self-similar with stationary increments processes…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…
This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A…
In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration $x$ will reach a set $B$ before a set $A$. This paper introduces an efficient and interpretable…
We study the functional link between the Hurst parameter and the Normalized Total Wavelet Entropy when analyzing fractional Brownian motion (fBm) time series--these series are synthetically generated. Both quantifiers are mainly used to…
We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in…
For equidistant discretizations of fractional Brownian motion (fBm), the probabilities of ordinal patterns of order d=2 are monotonically related to the Hurst parameter H. By plugging the sample relative frequency of those patterns…
In this paper, we describe a general method for constructing the posterior distribution of an option price. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as…