Related papers: Nonparametric estimation of scalar diffusions base…
We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock…
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which…
We consider a space structured population model generated by two point clouds: a homogeneous Poisson process $M$ with intensity $n\to\infty$ as a model for a parent generation together with a Cox point process $N$ as offspring generation,…
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
We propose a new simple and explicit numerical scheme for time-homogeneous stochastic differential equations. The scheme is based on sampling increments at each time step from a skew-symmetric probability distribution, with the level of…
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…
Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and…
The distributional single index model is a semiparametric regression model in which the conditional distribution functions $P(Y \leq y | X = x) = F_0(\theta_0(x), y)$ of a real-valued outcome variable $Y$ depend on $d$-dimensional…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
Time-dependent diffusion behavior is probed over sub-millisecond timescales in a single shot using an NMR static gradient, time-incremented echo train acquisition (SG-TIETA) framework. The method extends the Carr-Purcell-Meiboom-Gill (CPMG)…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…