Results 91 to 100 of about 51,428 (221)
Boundary differentiability for inhomogeneous infinity Laplace equations
Electronic Journal of Differential Equations, 2014 Summary: We study the boundary regularity of the solutions to inhomogeneous infinity Laplace equations. We prove that if \(u\in C(\bar{\Omega})\) is a viscosity solution to \(\Delta_{\infty}u:=\sum_{i,j=1}^n u_{x_i}u_{x_j}u_{x_ix_j}=f\) with \(f\in C(\Omega)\cap L^{\infty}(\Omega)\) and for \(x_0\in \partial\Omega\) both \(\partial\Omega\) and \(g:=u|_{
openaire +2 more sources
Mesh‐Based Charge Simulation Method and Its Applications to Electrostatic Electric Field Computation
High Voltage, EarlyView.ABSTRACT The charge simulation method (CSM) is a well‐established numerical technique employed in electrostatic field calculations, primarily due to its simplicity and computational efficiency. However, conventional CSM face challenges when applied to complex geometries, as they necessitate meticulous manual placement of simulation charges and matching
Tahan Wang +5 more
wiley +1 more source
A Bayes factor framework for unified parameter estimation and hypothesis testing
British Journal of Mathematical and Statistical Psychology, EarlyView.Abstract The Bayes factor, the data‐based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter estimation.
Samuel Pawel
wiley +1 more source
Real‐Time Conformal Maps and Parameterizations
Computer Graphics Forum, EarlyView.Abstract We present a simple algorithm to conformally map between two simple and bounded planar domains based on the concept of harmonic measure, which is a conformal invariant. With suitable preprocessing, the algorithm is fast enough to compute all possible conformal maps (having three real degrees of freedom) between the two domains in real time in
Q. Chang, C. Gotsman, K. Hormann
wiley +1 more source
Cryptocurrency Bubbles and Costly Mining
International Economic Review, EarlyView.ABSTRACT This paper develops a model of a cryptocurrency by incorporating mining into the otherwise standard search‐theoretic monetary framework. As usual, multiple equilibria exist. To obtain a sharp prediction on whether a cryptocurrency' s value will last in the future, I propose a notion of equilibrium refinement based on the feature that mining ...
Kohei Iwasaki
wiley +1 more source
Discrete infinity Laplace equations on graphs and tug-of-war games
Calculus of Variations and Partial Differential EquationsWe study the Dirichlet problem of the following discrete infinity Laplace equation on a subgraph with finite width $$Δ_{\infty} u(x) = \inf_{y \sim x}u(y)+\sup_{y \sim x}u(y)-2u(x) = f(x).$$ We say that a subgraph has finite width if the distances from all vertices to the boundary are uniformly bounded.
Fengwen Han, Tao Wang
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Variance Matrix Priors for Dirichlet Process Mixture Models With Gaussian Kernels
International Statistical Review, EarlyView.Summary Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non‐parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted.
Wei Jing +2 more
wiley +1 more source
Superposition Property in Disjoint Variables for the Infinity Laplace Equation
We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infinity-Laplace equation in separate domains is a viscosity solution in the product domain.
Liu, Qing +2 more
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Specification Tests for Jump‐Diffusion Models Based on the Characteristic Function
International Statistical Review, EarlyView.Summary Goodness‐of‐fit tests are suggested for several popular jump‐diffusion processes. The suggested test statistics utilise the marginal characteristic function of the model and its L2‐type discrepancy from an empirical counterpart. Model parameters are estimated either by minimising the aforementioned L2‐type discrepancy or by maximum likelihood ...
Gerrit Lodewicus Grobler +3 more
wiley +1 more source
A Non‐Parametric Framework for Correlation Functions on Product Metric Spaces
International Statistical Review, EarlyView.Summary We propose a non‐parametric framework for analysing data defined over products of metric spaces, a versatile class encountered in various fields. This framework accommodates non‐stationarity and seasonality and is applicable to both local and global domains, such as the Earth's surface, as well as domains evolving over linear time or time ...
Pier Giovanni Bissiri +3 more
wiley +1 more source