What is stochastic calculus

Stochastic processes

Prof. Anton Wakolbinger

Summer semester 2016

lecture : 4 hours
Tuesday, Friday 12: 15-14: 00, room 711 gr., RM 10

Exercises: 2 hours.

Exercise groups
Registration for the exercise groups takes place in the first week of the lecture period between Monday, April 11, midnight and Friday, April 15, midnight via this link. The tutorials are led by Mr. Tim Jahn, Ms. Anna Kremer, Ms. Elisabeth Stenschke and Ms. Jasmin Straub; The exercise coordinator is Ms. Noela Müller. The first tutorials will take place on Wednesday April 13th, Friday April 15th and Tuesday April 19th, with tips on the first exercise sheet, which will be handed out on April 12th.

The course is primarily aimed at Bachelor students of Mathematics in the 4th semester. It is part of the specialization in stochastics, the starting point for a specialization in stochastics and part of the specialization in statistics, and should be attended parallel to the lecture "Introduction to Stochastic Financial Mathematics" if you specialize in financial mathematics. In the L3 Mathematics course, it can be introduced as the L3M-HM module. Interested students from other fields of study are also welcome.

Keywords to the content are:

  • Conditional Expectation and Martingales;
  • Markov chains in discrete and continuous time;
  • Brownian motion and stochastic calculus;
  • Poisson trials and their relatives.

    Basic knowledge about the scope of chapters 1-4 of the book Elementary Stochastics or the course of the same name is required.

    Additional notes:

    Elementary conditional expectation
    Measurability
    Foil measurability
    Slides integral and expected value
    Elementary about stopped (super) martingales
    Again about the stop sentence
    Probabilities of meeting and expected meeting times
    Probabilities of ruin
    Gaussian processes and Brownian motion
    The Ito formula

    Training and exam:

    From the first week of lectures onwards, an exercise sheet is given out every Tuesday. There are tips on the exercises in the following 4 tutorials, the deadline for submitting the written solutions is Friday, 10 days after the exercise sheet has been handed out. In the week following submission, the solutions will be presented and discussed in the tutorials.

    Exercise sheets: 1 2 3 4 5 6 7 8 9 10 11

    Points can be earned through active participation in the tutorials. These are converted into (maximum 10) bonus points at the end of the semester. You only get bonus points if you present solutions to exercises (or parts of them) in the tutorial at least twice in the semester. Anyone who also achieves 75% of the total possible exercise points over the entire semester receives the maximum number of 10 bonus points. 100 points can be achieved in the final written examination (exam). The bonus points are added to these exam points. The exam is passed if a total of at least 50 points is achieved.

    The exam took place on Friday, July 15, 2016 in room H IV (lecture hall building Gräfstrasse) from 12:30 p.m. to 2:00 p.m.

    The second exam took place on October 14, 2016 from 10:15 am to 11:45 am in the H IV.
    The date for viewing the exam is Wednesday, October 19, 2016, 1.30 p.m. to 2.00 p.m., in SR 107, 1st floor RM10.

    Literature:

  • Kersting, G., Wakolbinger, A., Stochastic Processes, Birkhäuser 2014 *

  • Brokate, M., Kersting, G., Measure and Integral; Birkhäuser 2011 *. English translation: Measure and Integral. Birkhäuser 2015.
  • Grimmet, G. R., Stirzaker, D. R., Probability and Random Processes, 3rd ed., Oxford University Press, 2001;
  • Klenke, A., Probability Theory, 3rd ed. Springer 2013 (2nd ed. 2008 *). English translation: Probability Theory: A Comprehensive Course. Universitext, Springer 2007.
  • Williams, D., Probability with martingales, Cambridge University Press, 1991. * Also available as an e-book in the university library.

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