Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs

In this paper we propose an acceptance-rejection sampler using stratified inputs as diver sequence. We estimate the discrepancy of the points generated by this algorithm. First we show an upper bound on the star discrepancy of order $N^{-1/2-1/(2s)}$. Further we prove an upper bound on the $q$-th moment of the $L_q$-discrepancy $(\mathbb{E}[N^{q}L^{q}_{q,N}])^{1/q}$ for $2\le q\le \infty$, which is of order $N^{(1-1/s)(1-1/q)}$. We also present an improved convergence rate for a deterministic acceptance-rejection algorithm using $(t,m,s)-$nets as driver sequence.