I think it is possible. You may use the concept of ito calculus or you try to approximate the solution of the SDE. Otherwise, you can use simulation of the formula.

Not sure i understand what you are asking. Is this a continous time or periodic time problem. Solving a differential equation usually implies a continous time variable. You seem to saying the random shock term is inhomogenous. Is it inhomogenous in the mean or variance or perhaps both. I personally do not like to call the random shocks “noise”. In many stochastic problems, the random element is the main determinant of the future. This is because of the feedback nature of the problem. I would need more info to properly respond.

Hi

Can you post the equation so we can see what it looks like ?

What information do you have on that noise ?

In the mean time, try looking for Weiner Processes and Ito's lemma, they will allow you to diffentiate stochastic processes in a rigourous way I think.

Nicolas Podvin Jack Lothian Basel M. Al-Eideh

I attached the instance equation of my problem.

the right side of this equation is the stochastic process which we know that as electrical noise.

one of the model for noise is Winner process which it is not differentiable, while white noise is defined as the derivative of winner process.

so we have to Integrate the sides of equation to solve this numerical equation.

I am looking for a stochastic process that has deffentiable property.

It will be easier for me because it will be simpler than integral form for numerical simulation.

thanks you for participation in my problem.