Solution techniques for pulse problems in non-linear stochastic dynamics

Advantages and disadvantages of available solution techniques for pulse pro blems in non-linear stochastic dynamics are discussed. First, random pulse problems, both, those which do and do not lead to Markov theory, are presen ted. Next, the analytical and analytically numerical techniques suitable fo r Markov response problems such as moment equations, Petrov-Galerkin and ce ll-to-cell mapping techniques are briefly discussed. Usefulness of these te chniques is limited by the fact that effectiveness of each of them depends on the mean rate of impulses. Another limitation is the size of the problem , i.e. the number of state variables of the dynamical system. In contrast, the applicability of the simulation techniques is not limited to Markov pro blems, nor is it dependent on the mean rate of impulses. Moreover their use is straightforward for a large class of point processes, at least for rene wal processes. (C) 2000 Elsevier Science Ltd. All rights reserved.