Stochastic Calculus and Applications (Lent 2019)

Time and Location: M-W-F, 9-10am; lectures in room MR5; example classes see below.

Lectures: Roland Bauerschmidt rb812, Example classes: Daniel Heydecker dh489

This course is an introduction to Itô calculus, in Part III of the Cambridge Tripos.


  • Stochastic calculus for continuous processes. Martingales, local martingales, semi-martingales, quadratic variation and cross-variation, Itô's isometry, definition of the stochastic integral, Kunita-Watanabe theorem, and Itô's formula.
  • Applications to Brownian motion and martingales. Lévy characterization of Brownian motion, Dubins-Schwarz theorem, martingale representation, Girsanov theorem, and Dirichlet problems.
  • Stochastic differential equations. Strong and weak solutions, notions of existence and uniqueness, Yamada-Watanabe theorem, strong Markov property, and relation to second order partial differential equations.
  • Applications and examples.


Example Sheets

The tentative dates and locations for the example classes are:

  • We 13 Feb, 2-4pm, MR3
  • We 27 Feb, 2-4pm, MR9
  • We 13 Mar, 2-4pm, MR9
  • Fr 3 May, 2-4pm, MR9
  • Revision class: Mo 20 May, 2-4pm, MR9
    [In the revision class, the exam questions from 2018 and 2017 will be discussed.]


I will mostly follow the following references: