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Curricular information is subject to change
On the completion of this module the student should be familiar with the fundamental concepts of Probability Theory which lead towards the deep mathematical theory of Stochastic Analysis. This includes independence, expectation, conditional expectation, stochastic processes, filtrations, martingales.
The student will develop their ability to deal with abstract concepts and to relate them to real world examples. The student's ability to realise and critique proofs and arguments will be enhanced.
Measure theoretic approach to probability theory; types of convergence for random sequences; independence of sigma algebras; Borel-Cantelli lemmas; laws of large numbers; conditional probability and expectation; martingale convergence theorems; optional stopping theorems for martingales. Time permitting, central limit theorems and/or Brownian motion.
|Student Effort Type||Hours|
|Autonomous Student Learning||
Students are strongly recommended to revise Introduction to Probability (STAT20110) and Measure Theory & Integration (MATH30360) prior to commencing the course.
|Description||Timing||Component Scale||% of Final Grade|
|Continuous Assessment: Homework sheets.||Throughout the Trimester||n/a||Standard conversion grade scale 40%||No||
|Examination: 2 hour exam.||2 hour End of Trimester Exam||No||Standard conversion grade scale 40%||No||
|Resit In||Terminal Exam|
|Autumn||Yes - 2 Hour|
• Group/class feedback, post-assessment
Not yet recorded.
|Lecture||Offering 1||Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33||Fri 13:00 - 14:50|
|Lecture||Offering 1||Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33||Thurs 16:00 - 16:50|