Related papers: Heat kernel and gradient estimates for kinetic SDE…
In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their…
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…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
This paper introduces a novel kernel density estimator (KDE) based on the generalised exponential (GE) distribution, designed specifically for positive continuous data. The proposed GE KDE offers a mathematically tractable form that avoids…
We derive estimates of the derivatives of the heat kernel on noncompact symmetric spaces and on locally symmetric spaces. Applying these estimates we study the $L^{p}$-boundedness of Littlewood-Paley-Stein operators and the Laplacian of the…
We study heat kernels of Schr\"odinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric L\'evy measures with radial decreasing profiles and potentials belong to Kato class. Our setting is fairly…
We present a model for generating probabilistic forecasts by combining kernel density estimation (KDE) and quantile regression techniques, as part of the probabilistic load forecasting track of the Global Energy Forecasting Competition…
For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all…
Special case calculations are presented, which can be used to put restrictions on the general form of heat kernel coefficients for transmittal boundary conditions and for generalized bag boundary conditions.
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…
We prove sharp estimates on heat kernels and Green functions for subordinate Markov processes with both discrete an continuous time, under relatively weak assumptions about original processes as well as Laplace exponents of subordinators.…
We prove Cameron-Martin type quasi-invariance results for the heat kernel measure of infinite-dimensional Kolmogorov and related diffusions. We first study quantitative functional inequalities for appropriate finite-dimensional…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
The purpose of this paper is to establish a new continuous-time on-diagonal lower estimate of heat kernel for large time on graphs. To achieve the goal, we first give an upper bound of heat kernel in natural graph metric, and then use this…
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov…
We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently…
We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…
We prove sharp pointwise heat kernel estimates for symmetric Markov processes associated with symmetric Dirichlet forms that are local with respect to some coordinates and nonlocal with respect to the remaining coordinates. The main theorem…