#c22.txt: April 13, 2015

Today was a nice day, so the class was outside, only using our
biological computers between our shoulders.

We defined the discrete (usual) integral 

Int(f(s,W_s),s) 

with respect to time, where f(s,x) is an expression in s and x, and W_s is
a specific sample space

and the Stochastic integral Int(f(s,W_s)dW_s).

We also derived Ito's famous formula

df(t,W_t)= f'(t,W_t)dW_t + f_t(t,W_t) dt + 1/2*f''(t,W_t) dt