My math notes - Part 1

Sequence

https://en.wikipedia.org/wiki/Sequence

Sequence is like list
Often write like this: $a_n, b_n, c_n$

Example: $\{(p_t, v_t)_{t=1,...,T}\}$ where $p_t$ is the price associated with tick t and $v_t$ is the volume associated with tick t. The so-called tick rule defines a sequence $\{b_t\}_{t=1,...,T}$ where

b_t= \begin{cases} b_{t-1} &\text{if \(\Delta{p_t}=0\)} \\ \frac{\Delta{p_t}}{\Delta{p_t}} &\text{if \(\Delta{p_t}\neq0\)} \end{cases}