We employ Bayesian statistics using the nested-sampling algorithm to compare and rank
multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess …

The present book is devoted to parameter estimation in diffusion continuous-time models
involving fractional Brownian motion and related processes. Our models extend and …

Fractional calculus has emerged as a powerful and effective mathematical tool in the study
of several phenomena in science and engineering. This text addressed to researchers …

Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools
necessary to characterize Gaussian processes. The book focuses on the particular case of …

We implement Bayesian model selection and parameter estimation for the case of fractional
Brownian motion with measurement noise and a constant drift. The approach is tested on …

We consider a family of fractional Brownian fields {BH} H∈(0, 1) on R d, where H denotes
their Hurst parameter. We first define a rich class of normalizing kernels ψ and we rescale …

Abstract Generalizations of the Ornstein–Uhlenbeck process defined through Langevin
equations, such as fractional Ornstein–Uhlenbeck processes, have recently received a lot of …

While the statistical inference of Vasicek processes driven by both Brownian motions and
fractional Brownian motions has a long history, the statistical analysis for the Vasicek model …

We consider the Langevin equation which contains an unknown drift parameter θ and where
the noise is modeled as fractional Brownian motion with Hurst index H∈(0,12). The solution …

Tempered fractional Brownian motion (TFBM) and tempered fractional Brownian motion of
the second kind (TFBMII) modify the power-law kernel in the moving average representation …