Stochastic Processes

General data

Course ID:	0600-MS2-1PS
Erasmus code / ISCED:	11.104 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Stochastic Processes
Name in Polish:	Procesy stochastyczne
Organizational unit:	(in Polish) Zakład Dydaktyki i Nowoczesnych Technologii w Kształceniu
Course groups:
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Prerequisites:	Measure and Integral Theory 0600-MS2-1TMC
Short description:	Course objectives: By the end of the course the student should have developed the skills to: determine stopping times; making decomposition of supermartingales; calculate Ito integrals.
Full description:	Course profile: academic Form of study: stationary Course type: obligatory Academic discipline: Mathematics, field of study in the arts and science: mathematics Year: 1, semester: 2 Prerequisities: none lecture 30 h. exercise class 30 h. Verification methods: lectures, exercises, consultations, studying literature, home works, discussions in groups. ECTS credits: 5 Balance of student workload: attending lectures15x2h = 30h attending exercise classes 15x2h = 30h preparation for classes 7x3h = 21h completing notes after exercises and lectures 7x2h = 14h consultations 12x1h = 12h the final examination: preparation.and take 12h + 3h = 15h control works: repeating the material and preparation 3x4h = 12h Quantitative description Direct interaction with the teacher: 75 h., 3 ECTS Practical exercises: 77 h., 3 ECTS
Bibliography:	1. P. Billingsley Probability and measure 2. I. Karatzas, S. E. Shreve Brownian Motion and Stochastic Calculus Springer 1991. 3. D. Revuz, M. Yor Continuous martingales and Brownian motion Springer 1999.
Learning outcomes:	Learning outcomes: Know the major theorems and their proofs related to stochastic processes, stopping times, convergence of martingales, decomposition of supermartingales, the Wiener process, Ito integrals and local martingales.K_W03, K_U01, K_U11,K_U12 Be able to use of stochastic processes to model real-world phenomena.K_U18, K_W15 Obtains the basic skills to creative developing theory of stochastic processes.K_K01, K_K02, K_K07
Assessment methods and assessment criteria:	The overall form of credit for the course: final exam

This course is not currently offered.

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