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My math notes - Part 1


Sequence

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

  • Sequence is like list
  • Often write like this: an,bn,cna_n, b_n, c_n

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

bt={bt1if Δpt=0ΔptΔptif Δpt0b_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}