Abstract.Many applications involving statistical simulation, such as Monte Carlo methods, require non-uniform random sequences. These are usually created by first generating a uniform sequence and then using techniques such as rejection sampling or transformation. In this paper we introduce a new method to directly generate, without transformation or rejection, some non-uniform pseudo-random sequences. This method is a group-theoretic analogue of linear congruential pseudo-random number generation. We provide examples of such sequences, involving computations in Jacobian groups of plane algebraic curves, that have both good theoretical and statistical properties.

Received: August 17, 2007

AMS Subject Classification: 14H40, 65C10, 65C05, 68W20

Key Words and Phrases: pseudo-random sequences, non-uniform sequences, Jacobian groups, stochastic simulation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 4