I would like to use the vsl random number generators in a parallel monte carlo simulation, ie the possibility to distribute the simulation on all processor cores. Regarding this I have 2 different cases: - In the first case I would like to accelerate a simulation by distributing it on multiple processor cores. For example, let s say I need to simulate 10000 runs with each run containing 5000 timesteps. That means that I need to generate 10000*5000 random variates. My simulation would look something like this:

#define SEED 1

#define BRNG VSL_BRNG_MCG31

#define METHOD VSL_RNG_METHOD_GAUSSIAN_ICDF

// initialize vsl random generator streamVSLStreamStatePtr stream;

double a=0.0,sigma=0.3;

errcode = vslNewStream( &stream, BRNG, SEED );

for(int i=0; i<9999; i++){// simulate one path by generating 5000 variates.

double r[5000];

vdRngGaussian( METHOD, stream, N, r, a, sigma );

for (int j=0;j<4999;j++){

// simulate random walk using the variates

}

}

I would like to parallelize the outer loop. My question is: is it safe to call vdRngGaussian from multiple threads? And am I guaranteed to have independant variates?

The second scenario would be to parallelize multiple simulations. In this case I would like to do one full simulation per thread and I need to to generate independant variates for all simulations. In this case my question would be what is the approach to generating the random variates? Should I use one rng per thread and initialize them with different seeds? I have been told that this is not the best way of getting independant variates. Another method would be to use the leapfrog method. What is best?

anwar