Ito Process

It is a generalized Wiener process in which the parameters a and b are functions of the variable x and t: $dx = a\times (x,t) dt + b\times (x,t) dz$

This is Markov because the value of x only depends on time t. Both the drift rate and volatility rate are changing overtime.

For the change $\Delta x$ in small time interval $\Delta t$,

$\Delta x = a\times (x,t)\Delta t + b\times (x,t) \sqrt{\Delta t}$