Related papers: Nonparametric estimation of the diffusion coeffici…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…
The global estimation problem of the drift function is considered for a large class of ergodic diffusion processes. The unknown drift $S(\cdot)$ is supposed to belong to a nonparametric class of smooth functions of order $k\geq1$, but the…
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends on some unknown parameter and the…
In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the…
This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the…
We estimate nonparametrically the spatially varying diffusivity of a stochastic heat equation from observations perturbed by additional noise. To that end, we employ a two-step localization procedure, more precisely, we combine local state…
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…
We take into consideration generalization bounds for the problem of the estimation of the drift component for ergodic stochastic differential equations, when the estimator is a ReLU neural network and the estimation is non-parametric with…
This paper deals with nonparametric estimators of the drift function $b$ computed from independent continuous observations, on a compact time interval, of the solution of a stochastic differential equation driven by the fractional Brownian…
This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along…
We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
The path-specific effect (PSE) is of primary interest in mediation analysis when multiple intermediate variables between treatment and outcome are observed, as it can isolate the specific effect through each mediator, thus mitigating…