Stochastic Processes Seminar

Tatjana

Wolfgang

WeiCarsten

Mirko

David

Stephan Eule

Jan

Prerequisites

● Stochastic space● Stochastic variables● Probability distributions and densities

● Contour integrals● Matrix algebra● Ordinary and partial differential equations

Stochastic Process● Is a collection or sequence of stochastic

variables indexed by a set T (time).● Discrete or continuous in time● Discrete or continuous in space

Neuronal Spike Train

Brownian Motion

Robert Brown (1773 – 1858)

Albert Einstein (1879 – 1955) Marian Smoluchowski (1872 – 1917)

Louis Bachelier (1870 – 1946)

Movement of pollen in water

Brownian Motion

Food color diffusion

Random Walk

p=1/2n=1/2

Stock Market

Self-Similarity

Normal Distribution

Movement of pollen in water

Anomalous Diffusion

Paul Pierre Lévy (1886 – 1971)

Sub-Diffusion Super-Diffusion

Movement of foraging animalsLevy Stable Distribution

Solar Flares

Trapping of charges in amorphous semiconductors - Montroll

Human mobility

Further Examples

Briggs-Rauscher reaction

Nucleation

Belousov Zhabotinsky reaction

Prey-Predator

Kramers escape rate theory

Schedule etc.

● 2 Credits per talk● Any questions left? They will be answered in

the upcoming talks:● Statistical Processes Seminar Homepage