Related papers: Nonparametric inference for fractional diffusion
The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in…
In this paper, high-order moment, even exponential moment, estimates are established for the H\"older norm of solutions to stochastic differential equations driven by fractional Brownian motion whose drifts are measurable and have linear…
We present regularity results for nonlinear drift-diffusion equations of porous medium type (together with their incompressible limit). We relax the assumptions imposed on the drift term with respect to previous results and additionally…
In this study, we develop an asymptotic theory of nonparametric regression for a locally stationary functional time series. First, we introduce the notion of a locally stationary functional time series (LSFTS) that takes values in a…
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…
We consider the estimation of the drift and the level sets of the stationary distri- bution of a Brownian motion with drift, reflected in the boundary of a compact set $S\subset R^d$ , departing from the observation of a trajectory of this…
We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends…
We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one…
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown…
We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…
The celebrated Einstein relation between the diffusion coefficient $D$ and the drift velocity $v$ is violated in non-equilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a…
In this paper, a linear model of diffusion processes with unknown drift and diagonal diffusion matrices is discussed. We will consider the estimation problems for unknown parameters based on the discrete time observation in high-dimensional…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We propose a practical empirical fitting function to characterize the non-Gaussian displacement distribution functions (DispD) often observed for heterogeneous diffusion problems. We first test this fitting function with the problem of a…
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…