09 Introduction to Stochastic Processes
Material:¶
Markov Chains Ch. 1 (the rest is not in the syllabus)
Matrix Algebra (Optional)
Session from 20/21:
Topics¶
The topics of this and next week require a bit of knowledge of matrices and matrix algebra. I recommend reading “Matrix Algebra” which is the chapter we use from the Linear Algebra course. If you already passed the Linear Algebra course (i.e. you are on your 7th semester), you will probably not need to worry about this prerequisite.
Stochastic processes are mathematical models used to describe the evolution of systems that involve randomness. The most important elements of stochastic processes are their underlying probability distributions and the properties of their randomness, such as stationarity, independence, and Markovianity. The probability distribution of a stochastic process describes the likelihood of different possible outcomes at any given time, while the properties of randomness determine how the outcomes are related to each other over time. Stochastic processes can be classified into discrete-time or continuous-time, and they can be used to model a wide range of phenomena, including financial markets, stock prices, traffic flow, weather patterns, and biological systems.
- What is a random/stochastic process (as opposed to a random variable)?
- Poisson process
- Random walk
- Markov chains
The first two items are not directly covered in the literature and will be based on what I go through during class.
Problems to be worked on in/after class:¶
None specifically, but do some Wiseflow exercises