Stochastic Processes

Seminar taking place in the summer term 2010 in the seminar room every Wednesday at 10 a.m. c.t., 4th floor of the Max-Planck-Insitute for Dynamics and Self-Organization, Bunsenstr. 10, Göttingen.

Overview

Brownian Motion on Sphere

Up to the end of the nineteenth century it was commonly thought that if all initial data could only be collected, one would be able to predict the future with certainty. We now know this is not the case, in at least two ways. Firstly, quantum mechanics within a quarter of a century gave rise to a change in paradigm: nature was no longer seen as being deterministic - stochasticity became a fundamental property of the laws of nature. Secondly, the concept of chaos has arisen in which even small deviations in initial conditions give rise to large deviations in the temporal evolution of a deterministic, chaotic system.

However, in every day life we are surrounded by many non chaotic phenomena, which are somewhat between deterministic and random. Furthermore, it can also be cunductive to describe large ensembles of similar elements which might behave deterministicly with stochastic methods as shown in statistical mechanics. Therefore, stochastic processes will give us a well suited approach to formally describe quite many phenomena of life.

In this seminar we want to review basic and advanced concepts of stochastic processes and apply them to selected physical, biological and economic problems.

The seminar is meant to be interdisciplinary, with students from all natural science backgrounds. Each participant is highly encouraged to give one of the talks, but those who just want to listen and learn are also welcome.

Schedule

The schedule will be updated regularly as more references and presentations become available.

Title (click for PDFs) Date Speaker Contact References (click for PDFs)
Introduction - History, What? Why? Examples! 07.04.10 Mirko, David - -
Introduction to the fundamental concepts (correlations, characteristic function, central limit theorem,...) 14.04.10 Tatjana, David, Martin & Mirko - Chapter 1 of Hannes Risken, The Fokker-Planck Equation: Methods of Solutions and Applications.
Fokker-Planck equations (FPE), Master equations and their interrelationship 21.04.10 Giovanni Tatjana -
Methods for FPEs and Langevin equations in one dimension (first passage times, hitting probabilities) 28.04.10 Andreas David -
Mathematical foundations of stochastic processes 05.05.10 Christian - -
Anomalous diffusion 12.05.10 David Lamouroux - -
CANCELED 19.05.10 - - -
(Novel) Concepts and their Applications
Schramm-Loewner evolutions 26.05.10 Stephan - -
Modeling stock prices - Black Scholes model 02.06.10 Frederik Carsten Chapter 5.1 and 5.2 in Paul and Baschnagel, Stochastic Processes: From Physics to Finance.
Stochastic neuron models 09.06.10 Sven Tatjana Tuckwell, Introduction to theoretical neurobiology, Volume 2
Optimal resolution of the state space of a chaotic flow in presence of noise 16.06.10 Predrag Cvitanovic - Optimal resolution of the state space of a chaotic flow in presence of noise
Moran processes with application to genetic drift 23.06.10 Jens David R.A. Blythe and A.J. McKane, Stochastic models of evolution in genetics, ecology and linguistics, J. Stat. Mech. (2007).
POSTPONED due to BCCN meeting 30.06.10 - - -
Stochastic resonance 07.07.10 Srinivas Mirko L. Gammaitoni et al., Stochastic Resonance, Rev. Mod. Phys. 70, 223-287 (1998).
Alternative topics, loose ends
Feynman Kac formula (Ito calculus) - Christoph David Wiegel, Introduction to Path-Integral Methods in Physics and Polymer Science.
Kramers escape rate theory with applications to flagella motor switching in bacteria - - Mirko -
Reaction-diffusion systems and pattern formation with applications to fluid mechanics and epidemiology - - Wolfgang Cross and Hohenberg, Pattern Formation outside of equilibrium.
Anomalous diffusion and fractal FPEs - - Stephan -
Fractional Brownian motion - - - -
Predator prey systems - - - Kurt Jabcobs, Stochastic processes for physicists.
Methods for FPEs and Langevin equations in higher dimension - - Wei Wei -
Extreme value statistics of stochastic processes with applications to ecology (convex hulls, home ranges) - - Mirko S. N. Majumdar et al., Random Convex Hulls and Extreme Value Statistics, J. Stat. Phys, 138, 955 (2010); S. N. Majumdar, Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records.

Organizers/Contact

You are welcome to contact any of the organizers by e-mail:

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