This course talks about probability and stochastic processes.
Since this is for undergraduate, we will review probability measures, random variables, expectation, independence, conditional probability and laws of large numbers.
Now, we aim to discuss in their course the following:
1. Martingales
Here we will talk about filtration, martingales, stopping times, and the Optional Stopping theorem, and topics on martingales inequalities (Doobs Martingale Inequalities. and convergence theorem)
2. Markov Chains
We talk about Classification of States, and Long time behaviour of Markov Chains
3. Stochastic Processes in Continuous Time
The Poisson process and Brownian motion
...and the finale is
3. Ito Stochastic Calculus
The Ito Stochastic Integral, its properties and the Ito Formula
If we have time, we will talk about SDEs.
- Teacher: Jayrold Arcede