Stochastic Calculus

Record the learning materials of the course - "stochastic calculus" in National Cheng Kung University.

Before starting to read this article, please install chrome extension: Github with MathJax, to ensure the correctness of formula format.

• Stochastic Calculus
  • Practice Cases
    • Example 2.5 (See more)
    • Example 3.31 (See more)
    • Poisson Distribution (See more)
    • Random Access Problem in Machine-to-Machine (See more)
    • Compound Random Variables
  • Some useful self-defined libraries
  • Presentation (on Course)
• Author

Mostly use C++ to do both simulation/mathematic work and validation.

Develop environment requirement:

• Operating System : ubuntu 16.04

	version
gnuplot	version 5.0 patchlevel 3
g++	gcc version 5.4.0 20160609 (Ubuntu 5.4.0-6ubuntu1~16.04.9)
make	GNU Make 4.1
astyle	Artistic Style Version 2.05.1

Practice Cases

Example 2.5 (See more)

Normal case	Increased simulation times

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Example 3.31 (See more)

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Poisson Distribution (See more)

	Merge Poisson Process	Split Poisson Process
Mathematic
Simulation

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Random Access Problem in Machine-to-Machine (See more)

Access Class Barring	Random Access

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Compound Random Variables

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Some useful self-defined libraries

Name	Description
parse_arg	parsing the argument from argc/argv
poisson	generating poisson distribution.
rand_gen	additional wrapper of different kinds of random number generator.
event_list	scheduling、storing event list, use for discrete event simulation process.

Presentation (on Course)

• Stochastic Properties of Random Waypoint Mobility Model

Author

• Kevin Cyu(瞿旭民), kevinbird61@gmail.com