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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