Let $W_t$ be a Wiener process and for $a\geq0$
$$\tau_a:=\inf \left\{ t\geq0: |W_t|=\sqrt{at+7} \right\}.$$
Is $\tau_a<\infty$ almost everywhere? What about $E(\tau_a)$ then?
Let $W_t$ be a Wiener process and for $a\geq0$
$$\tau_a:=\inf \left\{ t\geq0: |W_t|=\sqrt{at+7} \right\}.$$
Is $\tau_a<\infty$ almost everywhere? What about $E(\tau_a)$ then?