Suppose at  the process is at the origin and let  denote the probability of being  step up after  trials

 which is easily understood from Figure 10.13

Figure 10.13: Movement of stock price according which can be considered as random

Thus:

Let the time between step be  and let the jump size be  Here  which is a constant is equal to . Hence we have , i.e.,.

First set  and  and let us also consider . Then we can easily prove that