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| IST4013 | Stochastic Processes | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Zafer KÜÇÜK | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Had students conceptualize the randomness as processes, giving the necessary knowledge of probability especially for stochastic modeling and analyzing this models, introducing some of the stochastic processes those are used in stochastic modeling. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn random functions and stochastic process | 1,5,8,10,11 | 1 | | LO - 2 : | calculate numerical correlation function and expected stochastic value and its variance. | 1,5,8,10,11 | 1 | | LO - 3 : | learn the importance of conditions essential for the continuum, integral and derivation of stochastic process. | 1,5,8,10,11 | 1 | | LO - 4 : | receive theorical and practical information about stationary processes, processes with independent increment. | 1,5,8,10 | 1 | | LO - 5 : | receive skills about stochastic modelling under dependence condition. | 1,5,8,10,11 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Random variables, random vectors, conditional distributions, expected value and probability calculations by conditioning, classification of stochastic processes, family of finite dimensional distributions, mean, variance, covariance correlation functions of stochastic processes, independent and stationary increment of processes, counting processes, Bernoulli processes and numbers and times of successes for the Bernoulli processes, Poisson processes,
Markov chains, Markov property, transition probabilities and Chapman-Kolmogorov equations.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Probability spaces and its basic properties. | | | Week 2 | Random variables, random vectors, conditional distributions, expected value and probability calculations by conditioning. | | | Week 3 | Stochastic processes, classification of stochastic processes, trajectories, family of finite dimensional distributions, probability distribution on trajectory space and Kolmogorov existence theorem. | | | Week 4 | Mean, variance, covariance correlation functions of stochastic processes, independent and stationary increment of processes. | | | Week 5 | Counting processes, Bernoulli processes and numbers and times of successes for the Bernoulli processes. | | | Week 6 | Poisson processes and their characterization | | | Week 7 | Review and problem solved | | | Week 8 | Mid-term exam | | | Week 9 | Arrival times and waiting times distributions for the Poisson processes, conditional distribution of arrival times | | | Week 10 | decomposition of Poisson processes into finite number of independent counting processes. | | | Week 11 | Markov chains, Markov property, transition probabilities and Chapman-Kolmogorov equations. | | | Week 12 | Visiting a fixed state, distribution of the first visiting time and the number of visits of a state, classification of states. | | | Week 13 | Asymptotic properties of Markow chains. | | | Week 14 | Markov processes, Markov processes with two states, birth and death processes. | | | Week 15 | Review and problem solved | | | Week 16 | End-of-term exam | | | |
| 1 | Aliyev R., 2010; Stokastik Süreçler Teorisine Giriş, KTU Yayınları, Trabzon | | | |
| 1 | Çınlar E., 1997; Introduction to Stochastic Processes, Englewood Cliffs, N J. | | | 2 | Karlin S., Taylor H. E., 1998; An Introduction to Stochastic Modeling, Academic Press. | | | 3 | Khaniyev T., 2003; Markov Zincirleri, KTU Yayınları, Trabzon | | | 4 | Ross S. M., 1993; Introduction to Probability Models, Academic Press Inc., New York | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 10/11/2015 | 1,5 | 50 | | End-of-term exam | 16 | 28/12/2015 | 1,5 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 20 | 1 | 20 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 165 |
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