Subject DatasheetDownload PDF
|Budapest University of Technology and Economics|
|Faculty of Transportation Engineering and Vehicle Engineering|
|1. Subject name||Stochasic Processes in System Dynamics III.|
|2. Subject name in Hungarian||Sztochasztikus folyamatok a rendszerdinamikában III.|
|3. Code||BMEKOVJD011||4. Evaluation type||exam grade||5. Credits||4|
|6. Weekly contact hours||2 (0) Lecture||0 (0) Practice||0 (0) Lab|
|9. Working hours for fulfilling the requirements of the subject||120|
|Contact hours||28||Preparation for seminars||30||Homework||15|
|Reading written materials||15||Midterm preparation||0||Exam preparation||32|
|10. Department||Department of Aeronautics and Naval Architectures|
|11. Responsible lecturer||Dr. Zobory István|
|12. Lecturers||Dr. Zobory István|
|13. Prerequisites||recommended: BMEKOVJD009 - Stochasic Processes in System Dynamics I.
recommended: BMEKOVJD010 - Stochasic Processes in System Dynamics II.
|14. Description of lectures|
|Transfer system characterized by a stochastic differential equation. Convergence concepts for stochastic sequences. The derivative process of a stochastic process. Harmonic oscillator excited by a stochastic process. Analytic concepts with respect to the convergence in the mean square. The transfer theorem. Tracing back the limit value, the continuity, the differentiability and the integrability in the mean square sense, to the properties of the (deterministic) autocorrelation function of the process. Characteristics in the mean square sense for second order weakly stationary processes. Level exceeding circumstances with stochastic processes. Generating realisation functions of second order weakly stationary processes. Spectral representation of second order weakly stationary processes. The concept of random measure and the stochastic integral defined on the basis of it. Stochastic characterisation of deterministic functions. The Brown-motion process and the white-noise. Characterisation of the time history of stochastic processes. The theorem of iterated logarithm. Further features of the Brown-motion process. The continuity and non-differentiability of the Brown-motion process. Generalized functions and stochastic processes. Defining stochastic integral. The stochastic integral leads to martingals. The extended definition of the conditional expectation. The extended definition of the conditional probability. Non-anticipative functions. Solutions to stochastic differential equations. The Ito-type stochastic differential equation. Existence and unicity of the solution. Reqired properties for unuque solvability of stochastic differential equation systems. The question on the existence of a global solution. Autonom stochastic differential equation. Linear stochastic differential equation. The homogeneous case. The non-homo¬geneous case. The Ornstein-Uhlenbeck process|
|15. Description of practices|
|16. Description of labortory practices|
|17. Learning outcomes|
|18. Requirements, way to determine a grade (obtain a signature)|
|Accepted homework sent before the deadline and written exam.|
|19. Opportunity for repeat/retake and delayed completion|
|According to the TVSZ|
|20. Learning materials|
|1. Zobory, I.: Sztochasztikus folyamatok a rendszerdinamikában I. Kézirat. BME Vasúti Járművek és Járműrendszeranalízis Tanszék. Budapest, 2011.
2. Arnold, L.: Sztochasztikus differenciálegyenletek Tipotex, Budapest, 2013.
|Effective date||27 November 2019||This Subject Datasheet is valid for||Inactive courses|