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Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $\sigma>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we…

Statistics Theory · Mathematics 2022-06-13 Tetsuya Takabatake

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…

Statistics Theory · Mathematics 2012-06-08 Ning Lin , Sergey V. Lototsky

We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=\theta(t)X_tdt+\epsilon dW_t^{H,K}, X_0=x_0,0\leq t \leq T$$ where…

Statistics Theory · Mathematics 2024-06-13 B. L. S. Prakasa Rao

We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…

Statistics Theory · Mathematics 2017-07-25 A. V. Artemov , E. V. Burnaev

\noindent \textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process $X$ driven by a fractional Ornstein-Uhlenbeck process $V$, i.e. the pair of processes defined by the non-Markovian continuous-time…

Probability · Mathematics 2016-10-14 Brahim El Onsy , Khalifa Es-Sebaiy , Frederi G. Viens

We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena…

Statistics Theory · Mathematics 2017-11-13 S. Dachian , N. Kordzakhia , Yu. A. Kutoyants , A. Novikov

We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant…

Statistics Theory · Mathematics 2007-12-18 Arnaud Gloter , Marc Hoffmann

This research aims to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the…

We derive the strong consistency of the least squares estimator for the drift coefficient of a fractional stochastic differential system. The drift coeffcient is one-sided dissipative Lipschitz and the driving noise is additive and…

Probability · Mathematics 2018-03-06 Yaozhong Hu , David Nualart , Hongjuan Zhou

We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we…

Statistical Mechanics · Physics 2016-12-28 Carlo Cafaro , Sean Alan Ali

Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends crucially on the…

Statistical Mechanics · Physics 2026-02-16 Stefano Giordano , Fabrizio Cleri , Ralf Blossey

This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…

Statistics Theory · Mathematics 2019-12-04 El Omari Mohamed , Hamid El Maroufy , Christiane Fuchs

This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…

Probability · Mathematics 2020-08-03 Xi Geng , Cheng Ouyang , Samy Tindel

The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…

Statistics Theory · Mathematics 2025-01-29 Mohamed Ben Alaya , Houssem Dahbi , Hamdi Fathallah

The stratified proportional intensity model generalizes Cox's proportional intensity model by allowing different groups of the population under study to have distinct baseline intensity functions. In this article, we consider the problem of…

Statistics Theory · Mathematics 2008-12-18 Amélie Detais , Jean-François Dupuy

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…

Statistics Theory · Mathematics 2024-06-10 El Mehdi Haress , Alexandre Richard

Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…

Statistics Theory · Mathematics 2015-10-01 Grigory Alexandrovich , Hajo Holzmann , Anna Leister

We consider the problem of estimating unknown parameters in stochastic differential equations driven by colored noise, which we model as a sequence of Gaussian stationary processes with decreasing correlation time. We aim to infer…

Numerical Analysis · Mathematics 2024-12-30 Grigorios A. Pavliotis , Sebastian Reich , Andrea Zanoni

We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…

Probability · Mathematics 2025-05-13 Siragan Gailus , Ioannis Gasteratos

A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical…

Statistical Mechanics · Physics 2023-03-20 Ignacio Tapia , Gonzalo Gutiérrez , Sergio Davis