COMPUTER SIMULATION OF DIFFUSIONS DRIVEN BY ALPHA-STABLE LEVY MOTION

摘要

In this paper we demonstrate that with the use of numerical discretization methods and computer simulation techniques it is possible to construct approximations of stochastic integrals with integrators defined by cr-stable (stable) Levy motion. As a consequence, solving numerically stochastic differential equations involving such integrals, we obtain an effective method of approximate construction of a wide class of diffusions with jumps. Application of suitable statistical estimation techniques allows to describe evolution in time of densities for processes solving such equations. It is possible to demonstrate some features of diffusions driven by random measures with densities with heavy tails, to visualize the effect of jumps of trajectories, etc. Statistical and numerical methods applied together allow to construct solutions to the wide class of stochastic differential equations involving integrals with stable integrators, providing appropriate stochastic models for a broaden spectrum of real life problems. References: 11