Lecturer: Vassili Gelfreich

Term(s): Term 2

Status for Mathematics students: List C

Commitment: 30 lectures

Assessment: 100% 3 hour final examination

Assumed knowledge:

• Basic ideas of Probability Theory as in ST120 Introduction to Probability: Random variables, expectations, mean and variance, central limit theorem, law of large numbers.
• Some experience of stochastic processes. In past years about 80% of students had taken MA4F7/ST403 Brownian Motion (although this module will recap Brownian motion and only a few properties are needed). The modules ST202 Stochastic Processes or ST333 Applied Stochastic Processes would be valid alternatives.
• Measure Theory: This module will use the key weapons of rigorous measure theory (measurable functions, integrals, Fubini's Theorem, Dominated Convergence Theorem, Fatou's lemma) as seen in MA359 Measure Theory or ST350 Measure Theory for Probability. The module gives a chance to see these ideas in action, but it will not stress measure theoretic aspects.

Useful background: There will be links with material from several other modules: Solutions to elliptic and parabolic linear PDEs are very closely related, and students who have taken Additional Resources

Content: We will introduce stochastic integration, and basic tools in stochastic analysis including Ito’s formula. We will also introduce lots of examples of stochastic differential equations.

Books:
Laurence Evans: An Introduction to Stochastic Differential Equations.
Bernt Oksendall: Stochastic Differential Equations.