I found this arrow notation while reading about markov chain and random walks and dont understand this notation. I can't find the answer anywhere. Help?
{T0 < Tc} (slanted arrow up, from left bottom to right top) {T0 < T1}, T0 represents inf{n>=0: Xn=0}.
there's one with slanted arrow down too
On
$A_n\nearrow A$ means you have a nested sequence $A_1\subseteq A_2\subseteq\dots$ with $\bigcup_{n\in\mathbb{N}} A_n=A$. Similarly, $A_n\searrow A$ means $A_1\supseteq A_2\supseteq\dots$ with $\bigcap_{n\in\mathbb{N}} A_n=A$.
Of course you could change the indexing set from $\mathbb{N}$ to say $\mathbb{R}$.
As $c \to \infty$, the set $\{\tau_0 < \tau_c\}$ gets larger, presumably. So $\{\tau_0 < \tau_c\} \nearrow \{\tau_0 < \infty\}$ probably means $\bigcup_{c > 0} \{\tau_0 < \tau_c\} = \{\tau_0 < \infty\}$. For the other arrow, the sets get smaller, so it would be an intersection instead of a union.