# Preliminary Content Subject To Change - Will Be Updated Before The Lecture Starts!

# SS 22: Theory of Stochastic Processes

**Lecture**

(from 25.04 to 27.07)

- Monday 8:30-10:00 2503 PH HS 3
- Wednesday 12:30-14:00 2503 PH HS 3

To facilitate the planning of the lecture please register in the TUMonline portal

No lecture on:

- Monday, 06.06.2022 ('Pfingstmontag')

**Tutorials**

See TUM-Online here you can also register for the tutorials. Please distribute yourselfs such that the 2 groups have approximately equal size.

The tutorials will start on tbd

No tutorials on:

- Monday, 06.06.2022 ('Pfingstmontag')

Please visit one of the other groups if your tutorial does not take place

**Preliminary Content**

- definition of stochastic processes and basic assumptions for their use to describe physical (and biomolecular) processes
- setting up, solving, and simulating Master equations
- setting up, solving, and simulating stochastic differential equations
- setting up, solving, and simulating Fokker-Planck equations
- understanding and applying basic concepts of stochastic thermodynamics
- using approximation methods for the analysis of complex stochastic process

See also the module description

**Literature**

- C. Gardiner: 'Stochastic Methods: A Handbook for the Natural and Social Sciences' (Springer)
- N.G. van Kampen: 'Stochastic Processes in Physics and Chemistry' (North-Holland)
- H. Risken: 'The Fokker Planck Equation' (Springer)
- U. Seifert: 'Stochastic thermodynamics: From principles to the cost of precission'
- S. Ciliberto: 'Experiments in Stochastic Thermodynamics: Short History and Perspectives'
- H. Touchette: 'The large deviation approach to statistical mechanics'
- H. Touchette: 'A basic introduction to large deviations: Theory, applications, simulations'
- A. Wachtel et al.: 'Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics'
- B. Altaner et al.: 'Fluctuating Currents in Stochastic Thermodynamics II. Energy Conversion and Nonequilibrium Response in Kinesin Models'
- J. Parrondo et al.: 'Thermodynamics of information'
- C. Van den Broeck, M. Esposito: 'Ensemble and Trajectory Thermodynamics: A Brief Introduction'
- further literature will be announced during the lecture

**Exam**

- 1st exam: 01.08.2022, 13:45 2503 PH HS 3
- 2nd exam: 12.10.2022, 13:45 2503 PH HS 3

See also www.tum.de/en/about-tum/news/coronavirus/coronavirus-exams/ for further information on exams during the COVID-19 pandemic.

Registration:

You can register from 30.05.2022 00:00 until 30.06.2022 23:59 for the first and if necessary register from 12.09.2022 00:00 until 26.09.2022 23:59 for the second exam.

Viewing of exam papers:

- For first exam: tbd
- For second exam: tbd

**Test Exam**

To give you the chance to get an impression of a typical exam a test exam will be held instead of the lecture probably on tbd. It replaces the problem set of the corresponding week. Please be there a few minutes early so that we can start on time.

Please note that we will discuss the test exam during the tutorials, thus we will not hand out a solution for it

**Bonus**

There will be the possibility to obtain a bonus. It is subject to the following conditions:

- You have to register for a tutorial in TUM-Online.
- For at least 70% of the homework problems a resonable attempt to solve the question has to be made.
- A question counts as resonable attempted if your handed in homework shows that you made a substantial effort to solve the problem by using the theory presented in the lecture.
- The decision if a homework problem is resonable attempted is made by the corrector of the homework.
- You have to keep the returned homeworks and show them on demand.
- One of the homeworks will be replaced by a test exam which will be held during one of the lectures (date will be announced later). The problems from the test exam will count as normal homework problems towards the bonus.

Fulfilling these conditions at the end of the semester has the following consequences:

- The grade of a passed exam is improved by one step in the grading scale (0.3 or 0.4 respectively), e.g. a grade of 2.0 in the exam will be improved to 1.7, a grade of 1.7 to 1.3.
- A grade of 1.0 can not be improved.
- A grade on a failed exam can not be improved.
- The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition)

**Problem Sets**

Every week on Friday a problem set containing problems to be solved during the tutorial sessions and as homework is published in the moodle course of the lecture.

The questions marked with tutorial will be discussed and solved during the tutorial sessions.

The problems marked with homework are to be solved at home and handed in until Friday 12:00 pm (noon) in the following week (e.g. if the problem set is handed out on Friday 29.04.22, it needs to be handed in by Friday 06.05.22). They will then be marked (resonably attempted or not) by the tutors and handed back to you. To to hand in the problem sheets please use the provided functionality in moodle. Please make sure that

- you use the pdf file format
- the size of single pages is approximately A4

## Course Material

The material for the course (exercise sheets, script, etc.) can be found on the course moodle. To access it please register in TUM-Online for the lecture & tutorials, this should automatically register you for the moodle course (it may take a bit of time until the data is synchronized)