1. An Iterative Monte Carlo Scheme for Generating Lie Group-Valued Random Variables
- Author
-
Sergio Scarlatti and Mauro Piccioni
- Subjects
Statistics and Probability ,Applied Mathematics ,010102 general mathematics ,Monte Carlo method ,Lie group ,Markov chain Monte Carlo ,01 natural sciences ,Hybrid Monte Carlo ,Algebra ,010104 statistics & probability ,symbols.namesake ,symbols ,Applied mathematics ,Ergodic theory ,Monte Carlo integration ,0101 mathematics ,Invariant (mathematics) ,Random variable ,Mathematics - Abstract
In this paper a simple approximation scheme is proposed for the problem of generating and computing expectations of functionals of a wide class of random variables with values in a compact Lie group. The algorithm is suggested by the time-discretization of an ergodic diffusion leaving invariant the distribution of interest. It is shown to converge as the discretization step goes to zero with the iterations in a natural way. IMAGE PROCESSING; SPIN SYSTEMS; ERGODIC DIFFUSION AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 82C80 SECONDARY 68U10
- Published
- 1994