Syllabus
1. Continuous time stochastic processes, counting processes, martingales.
2. Cummulative risk function, risk intensity, independent censoring, compensator.
3. Doob-Meyer decomposition, predictability, predictable quadratic variation.
4. Stochastic integral with respect to a bounded variation martingales, predictable variation and covariation of stochastic integral.
5. Martingale central limit theorems, functional central limit theorem, Gaussian processes.
6. Localization and local martingales.
Annotation
Continuous-time martingales. Predictability.
Doob-Meyer decomposition of semimartingales. Counting processes and compensators.
Predictable variation. Martingale stochastic integrals.
Central limit theorem for martingale stochastic integrals.