Stochastic Processes: Data Analysis and Computer Simulation

Course
en
English
12 h
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  • Self-paced
  • Free Access
  • Fee-based Certificate
More info
  • 6 Sequences
  • Intermediate Level

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Course details

Syllabus

Week 1: Python programming for beginners
- Using Python, iPython, and Jupyter notebook
- Making graphs with matplotlib
- The Euler method for numerical integration
- Simulating a damped harmonic oscillator
Week 2: Distribution function and random number
- Stochastic variable and distribution functions
- Generating random numbers with Gaussian/binomial/Poisson distributions
- The central limiting theorem
- Random walk
Week 3: Brownian motion 1: basic theories
- Basic knowledge of Stochastic process
- Brownian motion and the Langevin equation
- The linear response theory and the Green-Kubo formula
Week 4: Brownian motion 2: computer simulation
- Random force in the Langevin equation
- Simple Python code to simulate Brownian motion
- Simulations with on-the-fly animation
Week 5: Brownian motion 3: data analyses
- Distribution and time correlation
- Mean square displacement and diffusion constant
- Interacting Brownian particles
Week 6: Stochastic processes in the real world
- Time variations and distributions of real world processes
- A Stochastic Dealer Model I
- A Stochastic Dealer Model II
- A Stochastic Dealer Model III

Prerequisite

Differential and integral calculus and Linear algebra at a 2nd year undergraduate level.

Instructors

Ryoichi Yamamoto
Professor, Chemical Engineering
Kyoto University

John J. Molina
Assistant Professor
Kyoto University

Editor

Kyoto University

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