Stochastic Processes

Major: Applied mathematics and computer science
Code of subject: 6.113.01.E.080
Credits: 5.00
Department: Applied Mathematics
Lecturer: DSc., Professor Mykhailo V. Tokarchuk
Semester: 7 семестр
Mode of study: денна
Learning outcomes: • to know basic characteristics of random processes, their classification, Markov and non-Markov processes, basic equations of Kolmogorov, Fokker-Planck, Langevin, as well as methods for constructing entropy of systems; • be able to calculate the basic characteristics of random processes: mathematical expectations, variance and correlation functions, as well as to obtain the basic equations of Kolmogorov, Fokker-Planck, Langevin and apply to the description of random processes in the systems under study; • to be aware about the application of basic concepts of the theory of random processes in various fields of knowledge, as well as in the disciplines of preparation of their professional direction.
Required prior and related subjects: prerequisites: • probability theory, • methods of mathematical physics; Co-requisites: ---.
Summary of the subject: Random processes. Basic concepts. Random events. Event flows. Markov processes. Markov processes as stochastic processes. Non-Markov processes. Entropy.
Assessment methods and criteria: • control work (40%); • final control (60%): final control work.
Recommended books: 1. Rozanov Yu.A. Sluchajnye processy . - M,: Nauka, 1979. 2. Skorohod A.V. Lekcіi z teorii vypadkovykh procesіv. - Kyiv: Nauka, 1979. 3. Ventcel' E.S., Ovcharov L.A. Teorija sluchajnyh processov i ee inzhenernye prilozhenija. M.: Nauka, 1991, 383s. 4. Tihonov V.I., Mironov M.A. Markovskie processy. M.: Sovetskoe radio, 1977, 488s. 5. Van Kampen N.G. Stohasticheskie processy v fizike i himii. M. Vysshaja shkola, 1990 6. Miller B.M., Pankov A.R. Teorija sluchajnyh processov. M. Fizmatlitizd., 2002. 7. Rudavs'kij Yu.K., Kostrobіj P.P., Lozins'kij O.Ju., Uhans'ka D.V. Elementy teorіi vypadkovykh procesіv. L'vіv, NU LP, 2004. 8. Kostrobіj P.P., Markovych B.M., Tokarchuk M.V. Elementy teorіi vypadkovykh procesіv. L'vіv, NU LP, Rastr-7. 2015.