MONTE CARLO OF TWO-DIMENSIONAL BROWNIAN SHEETS

Publisher Summary This chapter discusses Monte Carlo of two-dimensional Brownian sheets. A Brownian sheet with an r-dimensional parameter set is a mean zero Gaussian process, defined on the positive orthant of r-dimensional Euclidean space having covariance. Such processes arise as the limit of partial sum processes on an r-dimensional grid. The chapter presents the results of a Monte Carlo experiment in which approximations to Brownian sheets are obtained as partial sums of Normal (0,1) rvs. Accurate estimates of quantiles of M2 can be obtained by using the program with increased sample size, and estimates of quantiles for the tied down version of M2 can be obtained by suitably transforming the partial sum process.