Optimal Random Number Generator for Large Scale Applications

Randomness and random numbers are needed in a wide range of areas; they are of basic importance in computational statistics, in the implementation of probabilistic algorithms, and in related problems of statistical computing that have a stochastic ingredient like financial Modeling and artificial intelligence methods. In most applications, the actual relationship between successive points in a random sample has no physical significance; hence, randomness of the sample for approximating a uniform distribution is not critical. Quasi random (low discrepancy) sequences are designed to have better uniformity and perform better than pseudo random sequences. For higher dimensional stochastic processes, however, the quality of the quasi random sequences rapidly decreases. The focus of this research is to design optimal strategies for random number generations that will perform well in higher dimensions as well.