Stochastic Processes at CEU -- winter semester 2013/14


No. of Credits: 3
No. of ECTS credits: 6
Time Period of the course: Winter Semester
Prerequisites: Probability 1
Course Level: PhD
Syllabus: will be here.
Classes: Wednesdays from 12:00 in room 301.
Course Coordinator: Imre Péter Tóth.

THE FINAL EXAM will be an oral exam on Thursday, the 24th of April 2014, starting at 9:00. LIST OF QUESTIONS HERE.

Topics actually covered: Suggested literature (References):
  1. Specific chapters to some of the lectures:
  2. General:
Grading rules:
There will be three homework assignments -- roughly once in every four weeks -- worth 20% of the total score. A midterm exam focused on problem solving will be worth 30%, while the final exam, focused on theory will be worth 50%.

Requirements for "audit":
regular participation in class and a short oral account of the concepts and phenomena learned.

Just for the record: Planned schedule, far from what was actually covered:
week #whentopicremark
week 12014.01.15Introduction, overview. Finite dimensional distributions and construction of stochastic processes. Kolmogorov extension theorem.
week 22014.01.22Classification of stochastic processes, examples. Poisson process, Wiener process. Markov property, finite Markov chains.
week 32014.01.29Mixing and ergodicity of Markov chains. Countable Markov chains. Transience, recurrence, positive recurrence.class delayed until spring
week 42014.02.05Random walks on Z. The reflection principle and applications. Distribution of the maximum, arcsine law, return times, local time. Random walks on Z^d.
week 52014.02.12Renewal processes, renewal equations.
week 62014.02.19Discrete time martingales. Branching processes. Barabási-Albert graph model, preferential attachment.
week 72014.02.26Discrete time stochastic integration. Discrete Black-Scholes formula.
week 82014.03.05Brownian motion, Wiener process. Construction(s), regularity properties, scaling properties.
week 92014.03.12Markov chains in continuous time. Infinitesimal generator, exponential semigroup. Examples.
week 102014.03.19Filtrations and stopping times. Markov processes and martingales in continuous time.
week 112014.03.26Ito's stochastic integral. Motivation, definition, basic properties.
week 122014.04.02Stochastic differential equations. Definition, examples.