Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes

Janicki, Aleksand; Weron, A.

• Preliminary remarks; Brownian motion, poisson process, alpha-stable Levy motion; computer simulation of alpha-stable random variables; stochastic integration; spectral representations of stationary processes; computer approximations of continuous time processes; examples of alpha-stable stochastic modelling; convergence of approximate methods; chaotic behaviour of stationary processes; hierarchy of chaos for stable and ID stationary processes. Appendix - a guide to simulation.

". . .it is remarkably complete and includes full references to recent literature. "---The Royal Statistical Society"Throughout the book there are many references to the literature and a wealth of useful and interesting examples exhibiting various types of behavior. A C program presented in an appendix was used to carry out the simulations."---Zentralblatt fur Mathematik, 2000