Quasi-Regression Monte-Carlo Method for Semi-Linear PDEs and BSDEs

Monte Carlo and quasi-Monte Carlo methods

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...

On Monte Carlo and Quasi-Monte Carlo for Matrix Computations

Monte-Carlo and Quasi-Monte-Carlo Methods for Numerical Integration

We consider the problem of numerical integration in dimension s, with eventually large s; the usual rules need a very huge number of nodes with increasing dimension to obtain some accuracy, say an error bound less than 10−2; this phenomenon is called ”the curse of dimensionality”; to overcome it, two kind of methods have been developped: the so-called Monte-Carlo and Quasi-Monte-Carlo methods. ...

Monte Carlo and Quasi-Monte Carlo for Statistics

This article reports on the contents of a tutorial session at MCQMC 2008. The tutorial explored various places in statistics where Monte Carlo methods can be used. There was a special emphasis on areas where Quasi-Monte Carlo ideas have been or could be applied, as well as areas that look like they need more research.

Monte Carlo Extension of Quasi-monte Carlo

This paper surveys recent research on using Monte Carlo techniques to improve quasi-Monte Carlo techniques. Randomized quasi-Monte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasi-Monte Carlo methods to hi...