Ito and Stratonovich Solutions of the Linear Growth Model
Define Ito and Stratonovich processes with the same SDE

:
Find mean and variance functions for the Ito process:
The mean and variance functions for the Stratonovich process are different:
When

, the Ito solution almost surely converges to zero, i.e. the large

limit of probability that process value is

does not exceed

equals

:
Confirm it using simulations:
When

, the Stratonovich solution, however, almost surely diverges, i.e. the large

limit of the probability that process value

exceeds

equals

:
Confirm it using simulations: