Stochastic Processes: Data Analysis and Computer Simulation
week13_The Euler method for numerical integration Ryoichi Yamamoto

 Start_Stochastic Presesses

Ryoichi Yamamoto
Feb. 20, 2023 02:45 English

 week11_Using Python iPython and Jupyter notebook

Ryoichi Yamamoto
Feb. 20, 2023 08:37 English

 week12_Making graphs with matplotlib

Ryoichi Yamamoto
Feb. 20, 2023 07:30 English

 week13_The Euler method for numerical integration

Ryoichi Yamamoto
Feb. 20, 2023 10:37 English

 week14_Simulating a damped harmonic oscillator

Ryoichi Yamamoto
Feb. 20, 2023 07:44 English

 week21_Stochastic variables and distributionnfunctions

Ryoichi Yamamoto
Feb. 20, 2023 20:40 English

 week22_Gennerationg random numbers with Gaussian_binomiak_Poisson distributions

Ryoichi Yamamoto
Feb. 20, 2023 13:14 English

 week23_The central limiting theorem

Ryoichi Yamamoto
Feb. 20, 2023 15:28 English

 week24_Random walk

Ryoichi Yamamoto
Feb. 20, 2023 13:07 English

 week31_Basic knowledge of Stochastic process

Ryoichi Yamamoto
Feb. 20, 2023 13:23 English

 week32_Brownian motion and the Langevin equation

Ryoichi Yamamoto
Feb. 20, 2023 14:20 English

 week33_The linear response theory and the GreenKubo formula

Ryoichi Yamamoto
Feb. 20, 2023 11:28 English

 week41_Random force in the Langevin equation

Ryoichi Yamamoto
Feb. 20, 2023 09:01 English

 week42_Simple Python code to simulate Brownian motion

Ryoichi Yamamoto
Feb. 20, 2023 10:04 English

 week43_Simulations with onthefly animation

Ryoichi Yamamoto
Feb. 20, 2023 10:53 English

 week51_Distribution and time correlation

Ryoichi Yamamoto
Feb. 20, 2023 09:45 English

 week52_Mean square displacement and diffusion constant

Ryoichi Yamamoto
Feb. 20, 2023 08:59 English

 week53_Interacting Brownian particles_DTH

Ryoichi Yamamoto
Feb. 20, 2023 15:55 English

 week61_Time variations and distributions of real world processes

ohn J. Molina
Feb. 20, 2023 18:08 English

 week62_A Stochastic Dealer Model1

ohn J. Molina
Feb. 20, 2023 13:41 English

 week63_A Stochastic Dealer Model2

ohn J. Molina
Feb. 20, 2023 16:54 English

 week64_A Stochastic Dealer Model3

ohn J. Molina
Feb. 20, 2023 12:31 English
Details
 Faculty/
Graduate School  Graduate School of Engineering
 Note
 ■Sample Program https://youtube.com/playlist?list=PLD74lMZl_0Ga5e1UlD_ZqCjpykXR3a4dh
Syllabus
Instructor name  Instructors: Ryoichi Yamamoto & John J. Molina 


Outline and Purpose of the Course  The motion of falling leaves or small particles diffusing in a fluid is highly stochastic in nature. Therefore, such motions must be modeled as stochastic processes, for which exact predictions are no longer possible. This is in stark contrast to the deterministic motion of planets and stars, which can be perfectly predicted using celestial mechanics. This course is an introduction to stochastic processes through numerical simulations, with a focus on the proper data analysis needed to interpret the results. We will use the Jupyter (iPython) notebook as our programming environment. It is freely available for Windows, Mac, and Linux through the Anaconda Python Distribution. The students will first learn the basic theories of stochastic processes. Then, they will use these theories to develop their own python codes to perform numerical simulations of small particles diffusing in a fluid. Finally, they will analyze the simulation data according to the theories presented at the beginning of course. At the end of the course, we will analyze the dynamical data of more complicated systems, such as financial markets or meteorological data, using the basic theory of stochastic processes. 

Course Goals 


Schedule and Contents 


Course Requirements  In addition to the knowledge of introductory physics, basic knowledge of linear algebra, calculus (differential and integral), and partial differential equations must be mastered beforehand. 
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