Pseudo-Random Streams for Distributed and Parallel Stochastic Simulations on GP-GPU

International audienceRandom number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. In particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. This results in a situation where potential biases can be combined with performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to parallelize random streams correctly, in the context of GPU-enabled stochastic simulations

Abstract Good random number generators are (not so) easy to find

Every random number generator has its advantages and deficiencies. There are no ``safe' ' generators. The practitioner's problem is how to decide which random number generator will suit his needs best. In this paper, we will discuss criteria for good random number generators: theoretical support, empirical evidence and practical aspects. We will study several recent algorithms that perform better than most generators in actual use. We will compare the different methods and supply numerical results as well as selected pointers and links to important literature and other sources. Additional information on random number generation, including the code of most algorithms discussed in this paper is available from our web-server under th

On Weyl sums and skew products over irrational rotations

AbstractLet ϕ : [0, 1] → R have a Lipschitz-continuous derivative on [0, 1], ∫10 ϕ(t)dt = 0, let α ϵ R\Q and write ϕn(x) = ϕ(x) + ϕ({x + α}) + ⋯ + ϕ({x + (n − 1)α}), n ϵ N, x ϵ [0, 1[. In this paper results on the boundedness and the limit points of the sequence (ϕn(x))n ⩾ 1 are given. Further, ergodicity of the skew product (x, y) ↦ (x + α, y + ϕ(x)) on RZ×R is proved for certain classes of ϕ and α