Stochastic Calculus
Record the learning materials of the course - "stochastic calculus" in National Cheng Kung University.
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/res/ncku.jpg)
Before starting to read this article, please install chrome extension: Github with MathJax
, to ensure the correctness of formula format.
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
Normal case |
Increased simulation times |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/example2.5/simulation.png) |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/example2.5/simulation_large.png) |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/example3.31/example3_31.png)
|
Merge Poisson Process |
Split Poisson Process |
Mathematic |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/poisson_distribution/image/part_a.png) |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/poisson_distribution/image/part_b.png) |
Simulation |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/poisson_distribution/image/part_a_sim.png) |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/poisson_distribution/image/part_b_sim_Y_10000_3.000000_0.500000.png) |
Access Class Barring |
Random Access |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/m2m/image/part_a_100_30_0.100000.png) |
![](https://raw.githubusercontent.com/kevinbird61/stochastic-calculus-and-probability-model/master/m2m/image/part_b_10000_20_1_20_1.png) |
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)
Author