Code: Select all
\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage[english]{babel}
\newcommand{\for}{\text{for }}
\begin{document}
\begin{align*}
p^{00}_{p p'}&=
\begin{cases}
e^{-\lambda h}\,P_0(p'|p, n)& \for p_t\leq p_B (a_t=0)\\
e^{-\lambda h}\,P_0(p'|p=0, n) & \for p_t>p_B (a_t=1)
\end{cases}\\
p^{01}_{p p'}&=
\begin{cases}
(1- e^{-\lambda h})\,P_1(p'|p, n)& \for p_t\leq p_B (a_t=0)\\
(1-e^{-\lambda h})\,P_1(p'|p=0, n) & \for p_t>p_B (a_t=1)
\end{cases}\\
P^{10}_{p p'}&=
\begin{cases}
0 &\for p_t\leq p_B (a_t=0)\\
e^{-\lambda h}\, P_0(p'|p=0, n) &\for p_t>p_B (a_t=1)
\end{cases}
\end{align*}
\end{document}