What is a Stochastics Process?

A stochastics process is a time dependent random variable. In other words, it is a variable, not a “process” per se. 

The time that the variable depends on can be continuous or discrete. Continuous time is more complex, we’ll cover it later.

For the discrete case, suppose we let S be the random variable. Typically, we represent the value of S at a particular point as the value of S at the previous point plus an increment. In other words, 

S_t = S_t−1 + x_t

where x_t is the increment at time t.