This document defines and provides examples of stochastic processes. It discusses how stochastic processes are probability models used to describe phenomena that evolve over time or space. Examples given include simple random walks and blackjack games. The document also outlines several fields that utilize stochastic processes, such as science, engineering, finance, and economics. Specific applications of stochastic processes in electrical engineering are also provided, including in electrical grid management, smart grids, telecommunications, and Markov chains. The document concludes by noting that top universities offer graduate coursework in stochastic processes.

1. By: Tahir Riaz Sindhu
FA16-REE-004
Topic:

2. Stochastic
• The word stochastic comes from
the Greek (stokhos, "aim")
• It occurs in various professional
and academic fields.
https://en.wikipedia.org

3. Definition
• A Stochastic Process (or random
process) is a probability model used
to describe phenomena that evolve
over time or space.[1]
• Opposite of a Deterministic Process
[1] The Oxford Dictionary of Statistical Terms.

4. Examples
• Simple Walk
• Blackjack Game

5. • Researchers use the term stochastic
systems to describe the physical systems in
which the values of parameters, measurements,
expected input, and disturbances are uncertain
• Probability Theory says that a purely
stochastic system is one whose state is
randomly determined, having a random
probability distribution or pattern that may be
analyzed statistically but may not be predicted
precisely.
https://en.wikipedia.org

6. Stochastic systems and processes play a fundamental role
in mathematical models of phenomena in many fields
Science Engineering
Finance Economics
https://en.wikipedia.org

7. Uses of Stochastic Process in
different fields of Science
• Mathematical Theory
• Artificial Intelligence
• Natural Science
( Physics, Biology, Medicine, Geomorphology , Creativity )
• Computer Science
• Music
• Subtractive Color Reproduction
• Language And Linguistics
• Social Sciences
• Business ( Manufacturing , Finance , Media )
https://en.wikipedia.org

8. • Electrical Grid Management
• Smart grids
• Telecommunication
• Markov Chain
• Monitoring Network Congestion
Uses of Stochastic Process in
Electrical Engineering

9. Continuous-time
Markov Chain (CTMC)
• It is a continuous-time stochastic process
with the Markov property which means
that future behaviour of the model
depends only on the current state of the
model and not on historical behaviour.

10. Telecommunication
• When messages flow from a source to a
destination (end-to-end) through a network.
Network conditions are extremely stochastic
in nature.

11. • Stochastic Power Grid Analysis
Automation and Test in Europe Conference and Exhibition (DATE’05) 1530-1591/05 IEEE
• Stochastic Model for Power Grid Dynamics
Fortieth Hawaii International Conference on System Sciences, January 3-6, 2007, Big Island, Hawaii]

12. • Stochastic Information Management in Smart Grid
IEEE Paper
• Adaptive Stochastic Control for the Smart Grid
IEEE Paper
Google Images

13. Universities are Offering
Stochastic Process Course in
Graduate Programs Of

14. Asian Universities
• Manny top ranked Asian universities are offering
Stochastic Process course, for their Electrical Graduate
program
For Example
1. National UNIVERSITY OF SINGAPUR (Japan)
2. Tsinghua University ( China )
3. Comsats ( Pakistan)

15. According To “THE”
Ranking
 California Institute of Technology
Department of Electrical engineering (United States)
EE 164. Stochastic and Adaptive
 MIT University (Department of Electrical engineering )
6.265J Advanced Stochastic Processes
https://www.timeshighereducation.com/
According to “THE” top ranked engineering
universities of world are teaching Stochastic
Process” course to their Graduate students.
For Example

16. Conclusion
• This course aims to help students acquire both the
mathematical principles and the intuition necessary to
create, analyze, and understand insightful models for a
broad range of these processes. The range of areas for
which discrete stochastic-process models are useful is
constantly expanding, and includes many applications in
engineering, physics, biology, operations research and
finance.
• Studying this course helps to improve the quality of
research work for Electrical Engineers
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science