Multiplicative processes on the set of shifted primes (Q1592142)

The authors define stochastic processes with independent quotients in terms of a multiplicative function \(g(n)\). The concept of independent quotients is a multiplicative version of processes with independent increments. The underlying multiplicative function \(g(n)\) is assumed to have properties which are similar to those of the class \(H\) of Kubilius for the `additive part' \(\log|g^*(n)|\), where \(g^*(n)= g(n)\) except when \(g(n)=0\) in which case \(g^*(n)=1\). If, when normalized, \(g(n)\) has a limiting distribution then it is assumed to be nonsymmetric (the sum of \(1/p\) over those primes \(p\) for which \(g(p)< 0\) or \(=0\) is assumed to be finite). A general criterion is given for a stochastic process defined in terms of \(g(n)\), as its argument goes through the values \(p+1\), \(p\) prime, to converge to a process with independent quotients.