Related papers: Optimal convergence rates for the invariant densit…

The estimation of the L\'{e}vy density, the infinite-dimensional parameter controlling the jump dynamics of a L\'{e}vy process, is considered here under a discrete-sampling scheme. In this setting, the jumps are latent variables, the…

We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding…

Recently a considerable interest has been paid on the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…

We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…

Accelerated diffusion models hold the potential to significantly enhance the efficiency of standard diffusion processes. Theoretically, these models have been shown to achieve faster convergence rates than the standard $\mathcal…

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…

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…

This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

We study sufficient conditions for local asymptotic mixed normality. We weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhya Ser. A 1982) so that they can be applied to a wider class of statistical models including a…

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…

We construct a density estimator in the bivariate uniform deconvolution model. For this model we derive four inversion formulas to express the bivariate density that we want to estimate in terms of the bivariate density of the observations.…

Diffusion and flow models achieve high generative quality but remain computationally expensive due to slow multi-step sampling. Distillation methods accelerate them by training fast student generators, yet most existing objectives lack a…

We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degenerate noise. For the associated transfer…

This paper is devoted to the uniform vanishing damping limit of the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion. Firstly, we find that fractional stress tensor diffusion helps to reduce the global regularity of the…

In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic…

Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference…

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel.…