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İzmir Ekonomi Üniversitesi
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    GRADUATE SCHOOL

    Applied Mathematics and Statistics – With Thesis

    STAT 502 | Course Introduction and Application Information

    Course Name
    Stochastic Processes
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    STAT 502
    Fall/Spring
    3
    0
    3
    7.5

    Prerequisites
    None
    Course Language
    English
    Course Type
    Elective
    Course Level
    Second Cycle
    Mode of Delivery -
    Teaching Methods and Techniques of the Course Problem Solving
    Q&A
    National Occupation Classification -
    Course Coordinator -
    Course Lecturer(s)
    Assistant(s)
    Course Objectives This course aims to provide basic theory and applications of the theory of stochastic processes.
    Learning Outcomes

    The students who succeeded in this course;

    • will be able to define approximate stochastic process models for a given research problem.
    • will be able to do logical proofs of important theoratical results.
    • will be able to apply the theory of stochastic processes to model real random phenomena.
    • will be able to analyze birth-death processes.
    • will be able to solve kolmogorov differential equations.
    Course Description The topics covered in this course include the definitions and the classifications of stochastic processes, Poisson process, renewal theory, Markov chains and processes, Martingales and Brownian motion process.
    Related Sustainable Development Goals

     



    Course Category

    		Core Courses
    Major Area Courses
    Supportive Courses
    Media and Management Skills Courses
    Transferable Skill Courses

     

    WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

    Week Subjects Related Preparation
    1 Stochastic processes: Definition and classification “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    2 Poisson process “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    3 Interarrival and waiting time distributions “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    4 Renewal theory “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    5 Markov chains “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    6 Markov processes “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    7 ChapmanKolmogorov equations and classification of states “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    8 Branching processes “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    9 Continuous time Markov chains “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    10 Birth and death processes “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    11 Kolmogorov differential equations “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    12 Martingales “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    13 Brownian motion process “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    14 Queueing Systems “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    15 Semester review
    16 Final exam

     

    Course Notes/Textbooks

    “Stochastic Processes”, Sheldon M. Ross,Wiley, 2nd Edition, 1995.ISBN-13: 978-0471120629
    Suggested Readings/Materials

    “An Introduction to Stochastic Modeling” by S. Karlin and H.E. Taylor, Academic Press,3 edition 1998. ISBN-13: 978-0126848878

     

    EVALUATION SYSTEM

    Semester Activities Number Weigthing
    Participation
    Laboratory / Application
    Field Work
    Quizzes / Studio Critiques
    2
    10
    Portfolio
    Homework / Assignments
    1
    10
    Presentation / Jury
    Project
    Seminar / Workshop
    Oral Exams
    Midterm
    1
    25
    Final Exam
    1
    45
    Total

    Weighting of Semester Activities on the Final Grade
    4
    55
    Weighting of End-of-Semester Activities on the Final Grade
    1
    45
    Total

    ECTS / WORKLOAD TABLE

    Semester Activities Number Duration (Hours) Workload
    Theoretical Course Hours
    (Including exam week: 16 x total hours)
    16
    3
    48
    Laboratory / Application Hours
    (Including exam week: '.16.' x total hours)
    16
    0
    Study Hours Out of Class
    14
    6
    84
    Field Work
    0
    Quizzes / Studio Critiques
    2
    10
    20
    Portfolio
    0
    Homework / Assignments
    1
    5
    5
    Presentation / Jury
    0
    Project
    0
    Seminar / Workshop
    0
    Oral Exam
    0
    Midterms
    1
    30
    30
    Final Exam
    1
    38
    38
        Total
    225

     

    COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

    #
    		 Program Competencies/Outcomes
    * Contribution Level
    1
    2
    3
    4
    5
    1

    To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

     
    -
    -
    -
    -
    X
    2

    To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.
    -
    -
    -
    X
    -
    3

    To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.
    -
    -
    -
    -
    -
    4

    To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

     
    -
    -
    -
    X
    -
    5

    To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.
    -
    -
    X
    -
    -
    6

    To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.
    -
    -
    -
    -
    -
    7

    To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.
    -
    -
    -
    -
    -
    8

    To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

     
    -
    -
    -
    -
    -
    9

    To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

     
    -
    -
    X
    -
    -
    10

    To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

     
    -
    -
    -
    -
    -
    11

    To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.
    -
    -
    -
    -
    -

    *1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

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