Additive functions and stochastic processes. II (Q1092950)

This paper continues the author's investigations from his previous paper [Litov. Mat. Sb. 25, No.1, 97--109 (1985; Zbl 0565.60031)]. For additive functions \(h_j\), a suitable norm \(\beta(n)\), ``scaling'' \(y(t,n)\) and norm \(A(y,n)\), a stochastic process is defined by \[ H_n(m,t) = \beta(n)^{-1}\sum_{j}\sum_{\substack{p^{\alpha} \| m+a_j\| \\ p\leq y(t)}} h_j(p^{\alpha})-A(y(t),n). \] Conditions are given for the convergence of these processes to a process with independent increments.