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This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Let $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^t\sigma\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^t\mu\bigl(X(u)\bigr)\mathrm…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or…
We consider a degenerate system of three Brownian particles undergoing asymmetric collisions. We study the gap process of this system and focus on its invariant measure. The gap process is described as an obliquely reflected degenerate…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Subordinate diffusions are constructed by time changing diffusion processes with an independent L\'{e}vy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many…
Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…
We propose classical interferometry with low-intensity thermal radiation for the estimation of nonclassical independent Gaussian processes in material samples. We generally determine the mean square error of the phase-independent parameters…
A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
In the present paper, we focus on semi-parametric methods for estimating the absorption probability and the distribution of the absorbing time of a growth-fragmentation model observed within a long time interval. We establish that the…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified…
We deal with a planar random flight $\{(X(t),Y(t)),0<t\leq T\}$ observed at $n+1$ equidistant times $t_i=i\Delta_n,i=0,1,...,n$. The aim of this paper is to estimate the unknown value of the parameter $\lambda$, the underlying rate of the…
This work is concerned with the estimation of the intensity parameter of a stationary determinantal point process. We consider the standard estimator, corresponding to the number of observed points per unit volume and a recently introduced…
The purpose of the present work is to construct estimators for the random effects in a fractional diffusion model using a hybrid estimation method where we combine parametric and nonparametric thechniques. We precisely consider $n$…