Example of stochastic differential equations

[hkour]

hello to everyone,

I have a problem solving a stochastic differential equation of the form:

dX/dt=aX²+bX+c+sXn(t),

where n(t) is white noise with a mean value equal to 0 and variance equal to one.

Does anyone know the solution of this stochastic differential equation or how to solve it?

Thank you

 

[pmsrw3]

Without that quadratic term, this would be easy, but...

Where does this come from? What exactly do you need? Do you need a full solution, or would it be good enough to predict the mean of X?

 

[hkour]

the stationary pdf of X gives the inverse gaussian distribution.
I need the full solution