Let $\{W_t^0, W_t^1 : t \geq 0\}$ be a 2-dimensional Brownian motion issued from zero. For every $r \in (-1,1)$, we define the stochastic process $$W_t^r = rW_t^1 + \sqrt{1-r^2}W_t^0, \quad t \geq 0, r \in ]-1, 1[.$$ $\mathcal{F}_t = \sigma(W_u^0, W_u^1 : u \leq t) \vee \mathcal{N}$, where $\mathcal{N}$ is the $\mathbb{P}$-null set of $\mathcal{F}$. I have to determine which of the following random variables are stopping times for every $r \in ]-1,1[$.
$A = inf \{t \geq 0 : W_t^1 + W_t^r = 5 \}$,
$B = inf\{t \geq 2 : W_t^1 = W_t^r\}$,
$C = sup\{t \leq 1 : W_t^1 < W_t^r\}.$
I know that I should check whether $\{T \leq t \} \in \mathcal{F}_t$, but I don´t know how. Does anyone has an idea ?
Thanks for your help.