Computer simulation of stochastic models with SDE-Solver software package

Authors:
Aleksander Janicki;Adam Izydorczyk;Przemyslaw Gradalski
Affiliations:
Mathematical Institute, University of Wrocław, Wrocław, Poland;Institute of Mathematics, Wrocław University of Technology, Wrocław, Poland;Institute of Mathematics, Wrocław University of Technology, Wrocław, Poland
Venue:
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Year:
2003

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Abstract

The SDE-Solver software package is our own professional C++ program, designed as a scientific computing tool serving for computer construction of solutions to a wide class of systems of stochastic differential equations (SDEs), including a broad class of diffusions with jumps driven by a number of non-Gaussian random measures. It has been developed as an application to the Windows system and its shareware version is available with a monograph. In this paper we shortly explain what new ideas have been used in order to get useful statistical and visual information on the time evolution of stochastic processes serving as solutions to such SDEs. Monte Carlo simulations, statistical estimation methods, approximate numerical algorithms, and modern computer visualization techniques applied together allow for constructing solutions to the wide class of semimartingale stochastic differential equations. In this way the SDE-Solver package (as other scientific computing tools) can be successfully applied in searching for proper and reliable stochastic models of real-life phenomena subject to random non-Gaussian disturbances and in studying their various properties.