Subject Datasheet
Download PDFBudapest University of Technology and Economics | |
Faculty of Transportation Engineering and Vehicle Engineering |
1. Subject name | Stochasic Processes in System Dynamics I. | ||||
2. Subject name in Hungarian | Sztochasztikus folyamatok a rendszerdinamikában I. | ||||
3. Code | BMEKOVJD009 | 4. Evaluation type | exam grade | 5. Credits | 4 |
6. Weekly contact hours | 2 (0) Lecture | 0 (0) Practice | 0 (0) Lab | ||
7. Curriculum | PhD Programme |
8. Role | Basic course |
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9. Working hours for fulfilling the requirements of the subject | 120 | ||||
Contact hours | 28 | Preparation for seminars | 30 | Homework | 0 |
Reading written materials | 30 | 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: BMEKOVJD001 - Analitical Methots in System Technique I. | ||||
14. Description of lectures | |||||
Stochastic excitation of a deterministic dynamical system model. Deterministic excitation of a stochastic dynamical system model: the output as a stochastic process. Horisontal and vertical characterisation of a stochastic process. The probability field. Operations among events. The relative frequency. The Lebesgue-type probability field. Roperties of the probability measure. Cpnditional probability. Conditional probability field. Conditional probability with respect to a zero probabilty condition event. Independence of events. Pair-wise and complete independence of the elements of event sequences. Complete set of events. The theorem of complete probability. The Bayes theorem. The mapping of the set of elementary events on a linear space. The linear space of random variables. Norm of linear spaces. Completeness of linear spaces. Banach spaces. Unitary linear spaces. Hilbert spaces. Real-valued, complex-valued vector-valued random variables. Stochastic sequence, stochastic process. Probability distributions, distribution function, basic properties, applications. Frequently used probability distributions. Probability density functions. Generalised density functions. Frequently used density functions. Characterisation of random variables by numerical values. Expectation, standard deviation and higher momentums. Random variables in L2. Characterisation of the Borel-measurable functions of random variables. Conection between the generator function and the characteristic function. Markov- and Cheishev-unequalities. Distribution function and density function for vector valued random variables. Marginal distribution function and density function. Expected vector and standard deviation matrix. Covariance and correlation. Condirtional distribution function and density function. Special case of zero probability condition. Conditional expectation. Regression function. Connection between two random variables. Pair-wise and complete independence of random variables. Operations among random variables, distribution of sum, product, quotient of random variables. Convergence concepts for random variable sequences. The weak law of large numbers. Central limit theorem. | |||||
15. Description of practices | |||||
16. Description of labortory practices | |||||
17. Learning outcomes | |||||
A. Knowledge
B. Skills
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18. Requirements, way to determine a grade (obtain a signature) | |||||
Regular participation at the lectures 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. |
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Effective date | 27 November 2019 | This Subject Datasheet is valid for | Inactive courses |