Open AccessMethods for modeling the Ornstein-Uhlenbeck process
Author(s) -
Anatolii Pashko,
Tetiana Ianevych
Publication year - 2019
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/3.3
Subject(s) - ornstein–uhlenbeck process , process (computing) , process modeling , gaussian process , work in process , stochastic process , computer science , markov process , statistical physics , mathematics , langevin equation , gaussian , mathematical optimization , engineering , statistics , physics , operations management , quantum mechanics , operating system
Two methods of modeling for the Ornstein-Uhlenbeck process are studied in the work. This process has many applications in physics, financial mathematics, biology. Therefore, it is extremely important to have instruments for modeling this process to solve various theoretical and practical tasks. The peculiarity of this process is that it has many interesting properties: it is Gaussian process, is a stationary process, is a Markov process, it is a solution of the Langevin stochastic equation, etc. Each of these properties allows you to apply different methods to this process modeling. We have considered only two methods, although there are many more. One method uses the fact that this process is Gaussian. Another is based on the Fourier expansion. For both of these methods there were specific conditions are obtained when these models satisfy the given levels of accuracy and reliability.