I asked a previous related question here: First hitting time for a brownian motion with a exponential boundary
Now Let $B_t$ be the standard Brownian Motion. Is the distribution/density of the first hitting time of $B_t$ for two exponential decaying boundaries known?
Trying to be more formal, if
$$T=\inf\{t\geq0,\vert B_t\vert \geq e^{-\lambda t}\}$$ with $\lambda>0$, what is
$$E[T]$$
If it is known is it also known when, instead of a Brownian Motion, one has a simple Ornstein-Uhlenbeck Process with mean $0$?
Thank you very much
