Fast simulation of Gaussian random fields

Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis are presented.Comment: 15 pages, 8 figures. Typos corrected in Algorithm 3, Remark (4), Algorithm 4, Remark (5), and Algorithm 5, Remark (5

Construction of the Paths of Brownian Motions on Star Graphs

Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of star graphs are given.Comment: 36 pages. The material of our previous articles 1012.0733, 1012.0737, 1012.0739 has been re-organized. The present article is a self contained version of 1012.073

On a Dual Pair of Spaces of Smooth and Generalized Random Variables

A dual pair G and G* of smooth and generalized random variables, respectively, over the white noise probability space is studied. G is constructed by norms involving exponentials of the Ornstein-Uhlenbeck operator, G* is its dual. Sufficient criteria are proved for when a function on S(IR) is the S-transform of an element in G or G*

Limit Theorems for the Donsker Delta Function : an Example

Limit theorems of the type of the law of large numbers and the central limit theorem are established (in the sense of Hida distributions) for the composition of the Dirac distribution with the stochastic exponential of Brownian motion

Law of large numbers and central limit theorem for Donsker's delta function of diffusions I

Limit theorems in the space of Hida distributions, similar to the law of large numbers and the central limit theorem, are shown for composites of the Dirac distribution with solutions of one-dimensional, non-degenerate Itô equations

Erratum: Fast simulation of Gaussian random fields[Monte Carlo Methods Appl. 17 (2011), 195-214]

In the paper "Fast simulation of Gaussian random fields”, a typo occurred. Instead of it should read in Algorithm3.1, Remarkd). For convenience of the reader we reproduce below the complete corrected algorithm