Lévy process simulation by stochastic step functions (Q2870641)

The authors ``study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare it to the traditional Metropolis/Hastings method.'' The latter method produces subsequent values which are not independent, due to the acceptance/rejection nature of this algorithm. The advantage of the new method is that an uncorrelated Markov chain can be obtained. The authors ``apply this method to the simulation of Lévy processes, for which simulation of uncorrelated jumps are essential.'' Furthermore, they ``perform numerical tests consisting of simulation from probability distributions, as well as simulation of Lévy process paths.'' The processes under consideration ``include a jump-diffusion with a Gaussian Lévy measure, as well as jump-diffusion approximations of the infinite activity NIG and CGMY processes. To increase efficiency of the step function method, and to decrease correlations in the Metropolis/Hastings method, (they) introduce adaptive hybrid algorithms which employ uncorrelated draws from an adaptive discrete distribution defined on a space of subdivisions of the Lévy measure space.''