Finite-Dimensional Distributions of a Square-Root Diffusion

A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

Effect of Abutment Angulation and Material on Stress and Strain Distributions in Premaxillary Bone: A Three-Dimensional Finite Element Analysis

Background and Aim: Dental implants with angled abutments are often inserted in the anterior maxillary region due to the status of the residual ridge and aesthetic considerations. The purpose of this study was to assess stress and strain distributions in the premaxillary bone around dental implants by means of finite element analysis (FEA). Materials and Methods: Four three-dimensional (3D) fi...

The Square Root Law and Structure of Finite Rings

LetR be a finite ring and define the hyperbolaH = {(x, y) ∈ R × R : xy = 1}. Suppose that for a sequence of finite odd order rings of size tending to infinity, the following “square root law” bound holds with a constant C > 0 for all non-trivial characters χ on R:

Finite Sample Properties of EMM, GMM, QMLE, and MLE for a Square-Root Interest Rate Diffusion Model

Monte Carlo forecasting from CIR square root diffusion models

We compare empirical convergence of Monte Carlo and quasi Monte Carlo estimates of the H-period forecasts using the Cox-Ingersoll-Ross square root diffusion model. The behaviour of the quasi Monte Carlo estimates in high dimensions (H = 250) using both Euler scheme and the Brownian bridge discretisation is analysed. We find that quasi Monte Carlo estimator displays much higher convergence rate ...