PARMONC - A Software Library for Massively Parallel Stochastic Simulation

We assume that a functional of interest ϕ ∈ R is represented as an expectation of some random variable ζ: ϕ ≈ Eζ One evaluates the value of Eζ using a sample mean Eζ ≈ ¯ ζ = L −1 L i=1 ζ i where sample values ζ i are independent and identically distributed random variables having the same distribution as ζ. One also needs to evaluate a second moment Eζ 2 of the random variable Eζ 2 ≈ ¯ ξ = L −1 L i=1 ζ 2 i in order to estimate a variance of the random variable ζ and it's standard deviation Varζ ≈ ¯ σ 2 = ¯ ξ − ¯ ζ 2 , (Varζ) 0.5 ≈ ¯ σ A complex random variable my be represented as a function ζ = ζ(α α k are independent random variables (random numbers) which have uniform distribution on the interval (0, 1). Therefore, to calculate a 1 sample mean ¯ ζ (for some sample volume L) we need a finite set of independent random numbers R = {α 1 , α 2 ,. .. , α S }. We call a stochastic experiment a process of calculating the sample mean ¯ ζ (for some sample volume L) with a particular set of random numbers R. Using different set R 1 = {α 1 , α 2 ,. .. , α S1 } of random numbers that are independent of the random numbers from R, we get independent value of the sample mean. In other words, we perform the stochastic experiment independent of the first one. A confidential interval for the expectation Eζ is defined by a formula