Need help solving two stochastic differential equations

Hello, I'm new here, so I guess I should introduce myself. I'm a student at a math. finance course. We have some homework where we have to solve two stochastic differential equations, and I'm pretty stuck. Would love it if someone could show me how this is done! :)

The equations are the following:

Where b is a real constant.

Where alpha is a real constant.

Looking forward to hearing from you! :)

Re: Need help solving two stochastic differential equations

Hello,

For the first one, apply Ito's lemma to

And you should get

And hence

I must admit I kind of struggled when it came to finding . You know you have to apply Ito's lemma to some transformed , so just try out simple functions of that may cancel out the in the right hand side of the equation.

FYI, this looks like what is called a brownian bridge... (it's in the Wikipedia article)

Re: Need help solving two stochastic differential equations