AEROENG 8830
Transcript Abbreviation:
Rdm Dyn Syst
Course Description:
Elements of axiomatic theory of probability, measure theory, stochastic differential equations, and martingales. Study of tools, e.g., sequential Monte Carlo, stochastic linearization, moment closure, Fokker-Planck equations, parameter estimation.
Course Levels:
Graduate (5000-8000 level)
Designation:
Elective
General Education Course:
(N/A)
Cross-Listings:
(N/A)
Credit Hours (Minimum if “Range”selected):
3.00
Max Credit Hours:
3.00
Select if Repeatable:
Off
Maximum Repeatable Credits:
(N/A)
Total Completions Allowed:
(N/A)
Allow Multiple Enrollments in Term:
No
Course Length:
14 weeks (autumn or spring)
Off Campus:
Never
Campus Location:
Columbus
Instruction Modes:
In Person (75-100% campus; 0-24% online)
Prerequisites and Co-requisites:
Prereq: ECE 6001, or Grad standing in Mechanical or Aerospace Engineering, or permission of instructor.
Electronically Enforced:
No
Exclusions:
(N/A)
Course Goals / Objectives:
Fundamentals of deterministic dynamical systems; linear systems, linearization
Build the foundation of the axiomatic theory of probability as developed by Kolmogorov: sets, measurable spaces, conditional probability, random variables, expectations, conditioning, independence, convergence of random variables
Use of indirect tools for probabilistic analysis: Generating functions: moment generating functions, characteristic functions; limit theorems: laws of large numbers and central limit theorem
Develop basic understanding of random processes, starting with sources of uncertainty in dynamic systems. Focus initially on linear dynamic random systems, power spectral density, wide sense stationary processes
Build an in-depth understanding of Markov chains, their recurrence and stationarity. Develop the theory that leads to sampling algorithms, importance sampling, Markov chain Monte Carlo and stochastic optimization
Develop the theory and tools for continuous time stochastic processes: stochastic differential equations, Brownian motion, Monte Carlo simulations, Direct moment closure, stochastic linearization, Fokker-Planck equations and its stationary solutions
Check if concurrence sought:
No
Contact Hours:
| Topic | LEC | REC out-of-class | REC in-class | Weekly LAB out-of-class | Weekly LAB in-class |
|---|---|---|---|---|---|
| Deterministic Dynamical Systems | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Numerical Simulations and Linear Perturbation Theory | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Axiomatic Theory of Probability | 6.0 | 0.0 | 0 | 0.0 | 0 |
| Convergence of random variables | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Generating functions | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Random walks | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Limit Theorems | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Markov chains | 6.0 | 0.0 | 0 | 0.0 | 0 |
| Stationary solutions | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Sequential Monte Carlo, Markov chain Monte Carlo, Stochastic Optimization | 4.0 | 0.0 | 0 | 0.0 | 0 |
| Stochastic differential equations | 4.0 | 0.0 | 0 | 0.0 | 0 |
| Wiener process, Brownian motion | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Moment closure | 1.0 | 0.0 | 0 | 0.0 | 0 |
| Stochastic linearization | 1.0 | 0.0 | 0 | 0.0 | 0 |
| Fokker-Planck equations, stationary solutions | 2.0 | 0.0 | 0 | 0.0 | 0 |
| Total | 40 | 0 | 0 | 0 | 0 |
Grading Plan:
Letter Grade
Course Components:
Lecture
Grade Roster Component:
Lecture
Credit by Exam (EM):
No
Grades Breakdown:
| Aspect | Percent |
|---|---|
| Homework | 40% |
| Midterm | 20% |
| Final | 20% |
| Projects | 20% |
Representative Textbooks and Other Course Materials:
| Title | Author | Year |
|---|---|---|
| Probability and Random Processes | Geoffrey Grimmett and David Stirzaker | |
| Probability and Random Processes: with applications to Signal Processing | Henry Stark and John W. Woods |
ABET-CAC Criterion 3 Outcomes:
(N/A)
ABET-ETAC Criterion 3 Outcomes:
(N/A)
ABET-EAC Criterion 3 Outcomes:
| No outcome selected |
Embedded Literacies Info: