Section outline

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    General

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    • Announcements Forum
    • Reading List URL
    • Discussion Forum
    • Lecture Notes (30 Nov 2021) File

      This is a reference set of lecture notes by Z. Qian from 2021-22.

      I will develop my own lecture notes as the course advances. Please note that some notation, order of introducing objects and ways to explain them will differ. I will endeavour to post new notes here but it is likely to happen once the course concludes, so coming to lectures and taking notes is the best way to stay on top of the material this term.

    • Ito's original paper on SDEs (1942) File
    • Background Stochastic Calculus Lecture Notes File

      I attach here my old lecture notes for B8.2 covering all the continuous time background material, and more, needed for this course. Other versions of lectures notes for these courses are available on the courses' pages. Please note that important aspects of this background material will be recalled in the first lectures this term - I appreciate a number of students might have not studied this material.

    • Background PMM Lecture Notes File

      I attach here my old lecture notes for Probability, Measure and Martingales (B8.1) course. This covers all the measure theory/probability/discrete time martingales background material, and more, needed for this course. Other versions of lectures notes for these courses are available on the courses' pages. Please note that some of this material, indeed a lot of it, is not actually needed to follow the course. It is needed, indeed necessary, to have an in-depth understanding of all the mathematical details and nuances of rigorous proofs. I will comment on this in my first lectures. 

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    Course Materials

    • Problem Sheet 1 Assignment
      UPDATED!

      There are 4 problem sheets in total, this is the  first one, which is related to the lectures in week 1 and week 2. This sheet will not be marked.

      This sheet, as all the other ones, has problems grouped in Sections A, B and C. You are expected to attempt all the problems in Sections A&B, and try to have a good think about problems in Section C. I will post solutions to problems, or a selection thereof (most likely Section A&C), a week after the last class.
      Tutors will discuss a selection of problems in classes, but will mostly focus on the ones in Section B.

      This is the first version of Pb Sheet 1. I may decide to update it in function of how much material is covered in Lectures 3&4 next week (W2).
    • Problem Sheet 2 Assignment
      Opened: Saturday, 24 October 2026, 2:26 PM
      Sheet 2 is related to the material covered in weeks 3 and week 4.
      The first version has only sections A & B. I will upload an updated version later with Section C added in.
    • Sheet 0 Assignment

      It is difficult to prepare Sheet 0 for this course. Students taking the course come from different backgrounds. Do not worry if you can not go through these problem and if some things here appear entirely novel. Some questions are not necessarily representative of what’s coming (in particular there is a bit more measure theoretical aspects here than in the course itself) whilst other could well appear on later (actual) problem sheets. I would encourage everyone to come to the first lectures, where I will try my best to explain what is really needed.

      All that is related to Brownian motion, stochastic calculus, Itˆo’s formula and continuous martingales will be recalled in the course.

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    Intercollegiate Classes

    • Class Signup Class registration
      Registration start: Monday, 5 October 2026, 12:00 PM
      Registration end: Friday, 6 November 2026, 12:00 PM
    • Class Tutor's Comments Assignment

      Class tutors will use this activity to provide overall feedback to students at the end of the course.

      Not available unless: You have signed up to a class