In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to alpha-stable Levy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic...

We develop a new class of continuous-time models based on the solutions of tempered fractional Langevin equations for Ornstein–Uhlenbeck process driven by Levy noise. We present methods of simulation of sample paths of such processes. We show how to use such models in modeling short term...

In the paper Weron (1996, Statist. Probab. Lett. 28, 165-171), I gave a proof to the equality in law of a skewed stable variable and a nonlinear transformation of two independent uniform and exponential variables. The Chambers et al. (1976, J. Amer. Statist. Assoc. 71, 340–344) method of...

In this paper, we discuss the issue of estimation of the parameters of stable laws. We present an overview of the known methods and compare them on samples of different sizes and for different values of the parameters. Performance tables are provided.