Related papers: Simulation and estimation for the fractional Yule …
We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
The paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and…
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
Random fuzzy variables join the modeling of the impreciseness (due to their ``fuzzy part'') and randomness. Statistical samples of such objects are widely used, and their direct, numerically effective generation is therefore necessary.…
We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional L\'evy processes are defined by integrating…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the…
Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless,…
In this paper, we simulate sample paths of a class of symmetric $\alpha$-stable processes using their series expression. We will develop a result in the approximation of shot-noise series. And finally, we will get a convergence rate for the…
Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that…
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…