STA 4303 Stochastic Process Modelling

SubjectCat-NbrClassTermModeDescriptionUnitsCampus
STA4303203731, 2003ONCStochastic Process Modelling1.00TWMBA
Academic Group:FOSCI
Academic Org:FOS003
HECS Band:2
ASCED Code:010101

Contents


STAFFING:

Examiner: Ashley Plank
Moderator: Ron Addie



RATIONALE:

Stochastic modelling finds application in diverse fields such as reliability theory, insurance, manpower planning, computer networking, traffic management, epidemiology, and many others. Knowledge of the techniques of stochastic modelling is particularly useful to statisticians and applied mathematicians, as well as technologists, engineers and management scientists.


SYNOPSIS:

This course consists of techniques and applications of stochastic modelling. A prerequisite level of mastery of statistical theory to that covered in STA2301 Distribution Theory (or equivalent) is required and it is desirable that students should also have covered the stochastic modelling module of MAT3102 Advanced Engineering Mathematics A. Topics covered include branching processes, Poisson processes, Markov processes, renewal processes, random walks and queueing processes.


OBJECTIVES:

On completion of this course students should be able to:

  • recognise the relevance of the mathematical techniques presented in this course to real-world problems;

  • demonstrate the ability to apply these techniques to some real-world processes;

  • demonstrate a knowledge and understanding of a range of random processes including Poisson processes, Markovian processes, random walks, branching processes, renewal processes, queueing processes, and semi-Markov processes

  • be familiar with various computational methods used in probability theory.



    • TOPICS:


    DescriptionWeighting (%)
    1. Introduction. Generating functions; Laplace transforms and moment generating functions; Fourier transform and characteristic function; Riemann Stieltjes integration; random sums; branching processes; indicator variables.
    		 25.00
    2. Poisson processes. Properties; decomposition and addition; nonhomogeneous Poisson processes; compound Poisson processes; PASTA.
    		 15.00
    3. Renewal processes. Properties; renewal equation; forward and backward recurrence times; renewal-reward processes; stationary and transient processes; stochastic convergence; delayed renewal processes; discrete renewal processes; regenerative processes.
    		 20.00
    4. Discrete-time Markov chains. Classification of states; random walks; ergodicity and periodicity; absorbing chains; Markov renewal processes; reversible chains.
    		 20.00
    5. Continuous-time Markov chains. Birth-death processes; Kolmogorov forward and backward equations; absorbing chains; phase-type distributions; uniformization; introduction to Markov renewal and semi-regenerative processes.
    		 20.00

    TEXT and MATERIALS required to be PURCHASED or accessed:

    Books can be ordered by fax or telephone. For costs and further details use the 'Book Search' facility at http://bookshop.usq.edu.au by entering the author or title of the text.

    Kao, E 1997, Introduction to Stochastic Processes, Duxbury, Belmont, Calif.




    REFERENCE MATERIALS:

    Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.

    A number of suitable reference and textbooks are available from the USQ library and elsewhere and will be advised by the lecturer.




    STUDENT WORKLOAD REQUIREMENTS:

    ACTIVITYHOURS
    Assessment30
    Assignments30
    Examinations3
    Lectures39
    Private Study60
    Tutorial13


    ASSESSMENT DETAILS:

    DescriptionMarks Out ofWtg(%)RequiredDue Date
    ASSIGNMENT 110.0010.00Y04 Mar 2003(see note )
    ASSIGNMENT 210.0010.00Y04 Mar 2003(see note )
    ASSIGNMENT 310.0010.00Y04 Mar 2003(see note )
    ASSIGNMENT 410.0010.00Y04 Mar 2003(see note )
    ASSIGNMENT 510.0010.00Y04 Mar 2003(see note )
    EXAM - 3 HOUR RESTRICTED50.0050.00YEND S1(see note )
    NOTES:
    .
    The Examiner will advise due dates of this Assignment.
    .
    As in Note 1.
    .
    As in Note 1.
    .
    As in Note 1.
    .
    As in Note 1.
    .
    Examination dates will be available during the Semester. Please refer to Examination timetable when published.

    IMPORTANT ASSESSMENT INFORMATION

    1. Attendance requirements:
      It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
    2. Requirements for students to complete each assessment item satisfactorily:
      To complete each of the assessment items satisfactorily, students must obtain at least 50% of the marks available for each assessment item.
    3. Penalties for late submission of required work:
      If students submit assignments after the due date without prior approval then a penalty of 10% of the total marks gained by the student for the assignment will apply for each working day late.
    4. Requirements for student to be awarded a passing grade in the course:
      To be assured of a passing grade, students must demonstrate, via the summative assessment items, that they have achieved the required minimum standards in relation to the objectives of the course by satisfactorily completing all summative assessment items (the examination and assignments).
    5. Method used to combine assessment results to attain final grade:
      The final grades for students will be assigned on the basis of the weighted aggregate of the marks obtained for each of the summative assessment items in the course.
    6. Examination information:
      In a Restricted Examination, candidates are allowed access to specific materials during the examination. The only materials that candidates may use in the restricted examination for this course are: writing materials (non-electronic and free from material which could give the student an unfair advantage in the examination); calculators which cannot hold textual information (students must indicate on their examination paper the make and model of any calculator(s) they use during the examination; Translation dictionary. With the Examiner's approval, candidates may, take an appropriate non- electronic translation dictionary into the examination. This will be subject to perusal and, if it is found to contain annotations or markings that could give the candidate an unfair advantage, it may be removed from the candidate's possession until the appropriate disciplinary action is completed.
    7. Examination period when Deferred/Supplementary examinations will be held:
      Any Deferred or Supplementary examinations for this course will be held during the next examination period.
    8. University Regulations:
      Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/SECARIAT/calendar/Part5/ or in the printed version of the current USQ Handbook.

    ASSESSMENT NOTES

    9.Students must retain a copy of each item submitted for assessment. This must be produced within 24 hours if required by the Examiner.