Functional Poissonian limit theorem and its applications (Q1850760)

A functional Poissonian type limit theorem is proved for ``random step lines processes'' defined via sums of i.i.d. indicators with random coefficients. The proof of the convergence in distribution of such processes in the Skorokhod space is based on Skorokhod's convergence criterion. Since, however, the processes under consideration do not have independent increments, a new maximal inequality for polynomial distributions and a new multidimensional limit theorem for the latter have to be developed, too. Some applications are considered; for example, analogs of risk processes in insurance mathematics and their (asymptotic) ruin probabilities as well as lost data processes are discussed in some detail.