Stochastic Processes: Data Analysis and Computer Simulation

Description

In this course, you will learn:

• Python programming in its most basic form.
• Theoretical foundations of stochastic processes.
• Brownian particle simulation methods.
• Financial data analysis is one example of such application.

Syllabus:

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

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

3. Brownian motion 1: basic theories

• Basic knowledge of the Stochastic process
• Brownian motion and the Langevin equation
• The linear response theory and the Green-Kubo formula

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

5. Brownian motion 3: data analyses

• Distribution and time correlation
• Mean square displacement and diffusion constant
• Interacting Brownian particles

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

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