On rates of convergence of stochastic relaxation for Gaussian and non- Gaussian distributions (Q1176292)

The problem of simulation of probability measure \(\phi\) in high- dimensional space \(R^ n\) is considered. Bounds on the rate of convergence of stochastic relaxation procedure in \(L_ 2(R^ n,\phi)\) are obtained not only for Gaussian \(\phi\), but also for non-Gaussian \(\phi\) which are bounded permutations of Gaussian, \(\tilde\phi(x)=(\rho(x)/Z)\phi(x)\), where \(0<c<\rho(x)<C\). The results make use of a bound on the norm of product of projections in terms of angles between the corresponding subspaces and the fact that the operator generated by the stochastic relaxation process in \(L_ 2(R^ n,\phi)\) is a product of projections.