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}

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Ito Process

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