The course starts with a quick introduction to conditional expectation. Then, normal distribution, multivariate normal distribution and Brownian motion are defined and discussed carefully. Exercises and homework are based on a setup of high-frequency financial data estimation problems. This includes providing some basic tools of asymptotic statistics on the way.
Students must be familiar with Statistics I and II taught at Hiyoshi or the basics of probability theory (distribution, expectation, variance, Strong Law of Large Numbers, Central Limit Theorem).
The evaluation will be based on five homeworks (each counting for 20% of the final grade).
The class often follows the textbook Stochastic Calculus: An Introduction with Applications (from Gregory Lawler) book content (Ch 1-2). You can find notes. Also, you can check Wikipedia page on normal distribution.
Homework should be sent by email to me (with Object: [S2020Hi] LAST_NAME FIRST_NAME), where i is the homework index, after being converted to PDF format (with the format LastNameFirstName.pdf in Romaji/English) and not handwritten. Latex will be very appreciated, but not required. Any other typing language such as Word would work too. You can use Sharelatex where you can code directly online (and even share it with a friend). Also, you will have information for documentation and/or installing Latex at The Latex Project. Graded homework will be sent back by email to students, so that they can learn from their mistakes. As much as possible, I will also provide a detailed individual feedback in the email.