Related papers: On Conditional least squares estimation for the AD…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
We study the asymptotic and pre-asymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient $D_{\mathrm{eff}}$ is numerically determined by the asymptotic…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
We propose a new statistical observation scheme of diffusion processes named convolutional observation, where it is possible to deal with smoother observation than ordinary diffusion processes by considering convolution of diffusion…
In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results.
We consider ordinary least squares estimation and variations on least squares estimation such as penalized (regularized) least squares and spectral shrinkage estimates for problems with p > n and associated problems with prediction of new…
Accurate and efficient surrogate models for aerodynamic surface pressure fields are essential for accelerating aircraft design and analysis, yet deterministic regressors trained with pointwise losses often smooth sharp nonlinear features.…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
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…
In this paper, we consider the Littlewood-Offord problems in one dimension for the Curie-Weiss models. Let \[Q_n^{+}:=\sup_{x\in\mathbb{R}}\sup_{v_1,v_2,\ldots,v_n\geq 1}P(\sum_{i=1}^{n}v_i\varepsilon_i\in(x-1,x+1)),\]…
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to…
We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient…
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
The curvature of ODE trajectories in diffusion models hinders their ability to generate high-quality images in a few number of function evaluations (NFE). In this paper, we propose a novel and effective approach to reduce trajectory…
The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as…
The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the…
Numerical transport models based on the advection-dispersion equation (ADE) are built on the assumption that sub-grid cell transport is Fickian such that dispersive spreading around the average velocity is symmetric and without significant…