MF5: Diffusion Processes and their Stochastic Logarithms

Lecturer: Dr Aleksandar Mijatovic, Imperial College

Term: Spring 2010
Place: Room 139 Huxley Building
Time: Thursday 6-9pm
First meeting: 14 January 2010
Course Home Page: p://www2.imperial.ac.uk/~amijatov/LGS/StochLog.pdf

Syllabus:
• The fundamental theorems: Dambis, Dubins-Schwartz theorem, Girsanov’s theorem, Martingale
representation theorem.
• Engelbert-Schmidt theory for one-dimensional diffusions: Brownian and continuous semimartingale
local time, occupation times formula, E-S 0-1 law, weak (explosive) solutions for
SDEs, one-dimensional time-homogeneous diffusion processes (existence, uniqueness).
• Singularity and absolute continuity of measures on filtered probability spaces.
• One-dimensional diffusion processes and stochastic logarithms, characterisation of the martingale
property for diffusion processes that are stochastic logarithms, classification of NFLVR
and characterisation of bubbles in one-dimensional diffusion models.