Related papers: Improved nonparametric estimation of the drift in …
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with a measure-valued external force. We establish existence of nonnegative weak solutions satisfying gradient estimates, provided…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
This paper considers the problem of adaptive estimation of a template in a randomly shifted curve model. Using the Fourier transform of the data, we show that this problem can be transformed into a stochastic linear inverse problem. Our aim…
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…
In this paper,we consider a macro approximation of the flow of a risk reserve, The process is observed at discrete time points. Because we cannot directly observe each jump time and size then we will make use of a technique for identifying…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
In this article, we consider elliptic diffusion problems on random domains with non-smooth diffusion coefficients. We start by illustrating the problems that arise from a non-smooth diffusion coefficient by recapitulating the corresponding…
We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…
We consider the robust adaptive nonparametric estimation problem for a periodic function observed in the framework of a continuous time regression model with semimartingale noises.
We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to…
The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
We address the variational formulation of the risk-sensitive reward problem for non-degenerate diffusions on $\mathbb{R}^d$ controlled through the drift. We establish a variational formula on the whole space and also show that the…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…