DSC 706 - Stochastic Process For Data Science

Fall Semester- 3 credit hours (2-1-3)
Contact Information
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Course Description

This course focuses on the mathematical methods and models that are required to understand investigate models. Topics may include essentials of stochastic integrals and stochastic differential equations. Probability distributions and heavy tails, ordering of risks, aggregate claim amount distributions, risk processes, renewal processes and random walks, markov chains, continuous Markov models, martingale techniques and Brownian motion, point processes, diffusion models, and applications in various subject related data science.

Course Outcomes

Upon the completion of this course, the student will be able to:

  1. define and analyze the data structure by using the mathematical tools; - DSC: 1
  2. use mathematical models and solve for equilibrium. Also models will be used analyze the policies related to various research field. - DSC: 2,3,4
  3. analyze and critically evaluate from oral written, and visual materials.- DSC: 3,6,8
  4. have the ability to predict the effects of changes in any kind of policy related to investigated field. –DSC: 3,7,9,11

The course outcomes are assessed by using a case study, quizzes, two mid-term exams and a comprehensive final exam.

AVL Learning Outcomes:

Upon successful completion of the program, students will be able to:

  1. be competent in using appropriate mathematical modelling and come to decision with this data.
  2. define, formulate mathematicaly and analyze a complex data structure involving human, material, machinery, money, information, time energy elements and various others and design it under realistic constraints and conditions.
  3. design and conduct experiments wit mathematical tools, gather data, analyze and interpret results for investigating complex data structure and come to decision with this data.
  4. be proficient in mathematical analysis of data and data management and apply data science concepts and methods to solve problems in various field and come to decision with this data.
  5. use information technologies effectively with the knowledge of state-of-the art hardware, and software capabilities related to data modelling with mathematics.
  6. communicate effectively, using information technology and oral and written skills to enhance decision making process through better communication.
  7. make ethical and legal decisions by considering cultural differences.
  8. work efficiently in interdisciplinary and multidisciplinary teams by collaborating effectively, in addition to an individual effective working ability.
  9. enhance critical thinking skill by integrating relevant information, decision-making techniques, and concepts through the interdisciplinary data science area.
  10. recognize the importance of mathematical modelling for entrepreneurship, innovation sustainable development and various other fields.
  11. have knowledge of the global and social effects of mathematical modelling and proper modelling of the data in various field.


Required Text(s) and Materials
  1. Foundations of Mathematical & Computational Economics, Kamran Dadkhah, 2nd edition, Thomson South-Western (Cengage Learning)
  2. The instructor can provide some articles published in journals, case-studies and reading related to current issues in air cargo industry when needed.
Assessment Method(s) and Evaluation

Grading will be based upon 10 short exams, 1 mid-term exam, 1 term-project and 1 final exam.

Mid-term Exam:

This is 40% of the final average: The mid-term exam will be administered by means of the portal on the scheduled date. The mid-term exam will be an essay type exam. It consists of 4-6 questions. There will be 2 hours to complete it.

Final Exam:

This is 45% of the final average: A comprehensive final exam will be administered by means of the portal on the scheduled date. The final exam will be an essay type exam. It consists of 4-6 questions. There will be 2 hours to complete it.


Questions in the exams are designed to make sure that you understand the main concepts, tools and techniques. The types of questions on the exams will be similar to those asked in the study questions and the class materials covered during the class period. Since the final exam is cumulative, the materials covered after the second midterm exam will be given more weight in the final exam.
The evaluation of the mid-term and final exams will be as follows:
The scores will be given according to organization of information, language and grammar and content of the written exam. In the organization of information part, well organized information with well constructed paragraphs; subheadings provided (if needed); logical progression of ideas are essential. In the language and grammar part, fluent sentences, no grammatical spelling and punctuation errors, accurately presented materials and sources are crucial. In the content part, information that you provide has to relate clearly to the main topic and include supporting details and/or examples, clear well-focused topic. The main idea has to stand out and be supported by detailed information. Any mathematical argument should be supported with utmost detail and precision.


This is 15% of the final average: Students are required to complete 5 homeworks throughout the course by means of the portal. The homeworks are composed of ten questions with each homework covering a separate chapter. Due dates will be announced when homework is assigned. Late homework assignments will NOT be graded. There will be no make-up homework if you fail to complete it by the deadline.

Policy on Make- ups: Make-up examinations will only be administered to students with excused absences. Excused absences include death in the immediate family, University sponsored trips or critical illness. Verification is required and permission to miss an examination must be secured PRIOR TO the scheduled examination time. If this condition is not met, a zero will be given for the missed exam.

Grading Scale
Grade Quality Points
A = Excellent 90 – 100%
B = Good 80 – 89%
C = Satisfactory 70 – 79%
D = Passing 60 – 69%
F = Failing below 60%
Incompletes- I

Incompletes (I) demonstrate that a student was doing sufficient work at the end of a semester period but, for reasons beyond the control of the student, was unable to complete all requirements of the course in the related semester. The grade I obliges student to complete all course requirements within a time period that is specified by the instructor. This time period can’t exceed one academic calendar year from the end of the semester in that the grade I is assigned. The students has to arrange with the course instructor in order to complete all course requirements in a specified time period. If all course requirements are not completed by the students in a specified time period, I is changed to the grade F, unless the instructor has assigned a different grade.


Students may withdraw from courses following the drop and add period until mid-term by completing the withdrawal process on the portal. A grade of "W" will appear in the student's official records if the student has withdrawn according to the SFU’s Withdrawal Policy. (Please see the SFU’s Withdrawal Policy for details.)

Attendance Policy

Participation and consistent attendance is essential for acceptable performance in the course. The students are expected to be present each class period except when special hardships occur, e.g. death in the immediate family, University sponsored trips or critical illness.
Regulations for attendance of Suje Florida University will be applied for this class.

Academic Integrity

Academic integrity is the responsibility of all Suje Florida University faculty and students. Cheating and plagiarism are not tolerated and will result in a failing grade, if the student is found guilty of cheating. All students are expected to do the work on their own and to accept standards of academic ethics.

Course Expectations
  1. As a portal course, it requires extensive work be done by students using the Internet. You must familiarize yourself with your portal account. Supplemental materials, including lecture notes will be posted on portal.
  2. Students are expected to read assigned material(s) prior to lecture and participate in discussions and activities.
  3. Log on at least three times a week – on different days in order to completely weekly assignments, assessments, discussions and/or other weekly deliverables as directed by the instructor.
  4. Check your e-mail often.
  5. Communications with the instructor should be via portal or e-mail. Email is preferred. Emails sent Monday through Friday will be answered within 24 hours. Emails sent Saturday– Sunday may not be answered until Monday. If your email is not written in a respectful manner, you should not expect a response.
  6. It is your responsibility to ensure you are registered throughout the course.
  7. Discussion must always be civil. Rudeness or disrespect of other students will not be tolerated. We will respect the thoughts and opinions and others, even when we do not agree or believe the other person is terribly misinformed.
  8. Changes may be necessary in the syllabus. Students will be informed of changes to the syllabus.
  9. Students are responsible for any new material or announcements missed due to the absence.
Tentative Detailed Course Content and Recommended Readings
Week Topic Recommended Reading(s)

Stochastic integrals

Lecture notes available


Stochastic differential equations

Lecture notes available


Probability distributions and heavy tails

Lecture notes available


Ordering of risks

Lecture notes available


Aggregate claim amount distributions

Lecture notes available


Risk processes

Lecture notes available


Renewal processes and random walks

Lecture notes available


Markov chains Midterm

Lecture notes available


Continuous Markov models

Lecture notes available


Martingale techniques and Brownian motion

Lecture notes available


Point processes

Lecture notes available


Diffusion models

Lecture notes available


Asymptotic theory of nonstationary variables

Lecture notes available


Asymptotic theory of nonstationary variables: Brownian Bridge

Lecture notes available


Density Functions

Lecture notes available



Note: Essentials of and..Concepts from insurance and finance.....Applications to insurance and finance processes.

Student Opinion of Instruction

At the end of the term, all students will be expected to complete an online Student Opinion of Instruction survey (SOI) that will be available on portal. Students will receive an e-mail notification through their Suje Florida University e-mail address when the SOI is available. SOI responses are anonymous to instructors/administrators. Instructors will be able to view only a summary of all responses two weeks after they have submitted final grades.

Title IX Statement

Suje Florida University is committed to creating a diverse and inclusive work and learning environment free from discrimination and harassment. Discrimination on the basis of race, color, ethnicity, national origin, sex (including pregnancy status, sexual harassment and sexual violence), sexual orientation, gender identity, religion, age, national origin, disability, genetic information, or veteran status, in the Suje Florida University's programs and activities is prohibited as required by applicable laws and regulations such as Title IX. The individual designated with responsibility for coordination of compliance efforts and receipt of inquiries concerning nondiscrimination policies is the University's Title IX Coordinator.

Access Statement

Students with disabilities who are experiencing barriers in this course may contact the Access Office for assistance in determining and implementing reasonable accommodations.