Related papers: Optimal convergence rates for the invariant densit…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$…

We investigate robust parameter estimation and testing procedure for multivariate diffusion processes observed at high frequency via the minimum density power divergence estimator (MDPDE). Within a general diffusion framework and under…

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our…

This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a $d^*$-way…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…

We consider parametric estimation of the continuous part of a class of ergodic diffusions with jumps based on high-frequency samples. Various papers previously proposed threshold based methods, which enable us to distinguish whether…

Diffusion models have demonstrated great potential in generating high-quality content for images, natural language, protein domains, etc. However, how to perform user-preferred targeted generation via diffusion models with only black-box…

For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…

We consider a nonparametric regression model $Y=r(X)+\varepsilon$ with a random covariate $X$ that is independent of the error $\varepsilon$. Then the density of the response $Y$ is a convolution of the densities of $\varepsilon$ and…

We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter $\theta$. We suppose that the process is discretely observed at the instants (t n i)i=0,...,n with $\Delta$n = sup…

In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…

This paper provides a full characterization of the value function and solution(s) of an optimal stopping problem for a one-dimensional diffusion with an integral criterion. The results hold under very weak assumptions, namely, the diffusion…

We study the fundamental problem of estimating the mean of a $d$-dimensional distribution with covariance $\Sigma \preccurlyeq \sigma^2 I_d$ given $n$ samples. When $d = 1$, \cite{catoni} showed an estimator with error $(1+o(1)) \cdot…

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,…

We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…