  We present two approaches to establish the exponential decay of correlation
functions of Euclidean quantum field theories (EQFTs) via stochastic
quantization (SQ). In particular we consider the elliptic stochastic
quantization of the H{\o}egh--Krohn (or $\exp (\alpha \phi)_2$) EQFT in two
dimensions. The first method is based on a path-wise coupling argument and PDE
apriori estimates while the second on estimates of the Malliavin derivative of
the solution to the SQ equation.
