Aleksander Janicki

Computer simulation of diffusions driven by a-stable Le´vy motion

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 α-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.

Computer simulation of attractors in stochastic models with a-stable noise

The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to 2nd order stochastic differential equations, subject to large random external disturbances with infinite variance, described by α-stable Levy motion processes. This provides us with qualitative and quantitative information on their asymptotic behavior, and, in particular, with graphical visualization of stochastic attractors in appropriate phase spaces.