Simulation of Brownian motion by truncated multiplicative functions (Q1093674)

The value \(U_n(m,t)=d_n^{-1} h^{-}\sum_{k\leq th}\psi^{(n)}(m+k)\), \(0\leq t\leq 1\), \(h=h(n)\to \infty\) if \(n\to \infty\) may be considered as a stochastic process regarding some probability spaces. For some sequences of multiplicative functions \(\psi\^{(n)}\) it is shown that there exists \(h\) and \(d_n\) as well as \(U_n(m,t)\) which is called a model of Brownian motion. Sufficient conditions for this are given in this work.