# Computing the limit of the expectation of a function of a stochastic process (phew!)

I state my problem in a few lines then describe what I have already done.

I have a quite simple stochastic differential equation (SDE):

$dx=-2x \, dt+\sqrt{1-x^2} \, dW$ with $W$ a brownian.

I want to compute $\displaystyle{\lim_{t\to 0}}~\mathbb{E}\left[B_t\tanh\left(A_t\frac{x(t)-x(0)}{t}\right)|x(0)\right]$ and can't manage to do it.