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 

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 Lebesguetype 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. Pairwise 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. Realvalued, complexvalued vectorvalued 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 Borelmeasurable functions of random variables. Conection between the generator function and the characteristic function. Markov and Cheishevunequalities. 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. Pairwise 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


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. 

Effective date  27 November 2019  This Subject Datasheet is valid for  Inactive courses 