  In this note we first consider local times of random walks killed at leaving
positive half-axis. We prove that the distribution of the properly rescaled
local time at point $N$ conditioned on being positive converges towards an
exponential distribution. The proof is based on known results for conditioned
random walks, which allow to determine the asymptotic behaviour of moments of
local times. Using this information we also show that the field of local times
of a reflected random walk converges in the sense of finite dimensional
distributions. This is in the spirit of the seminal result by Knight(1963) who
has shown that for the symmetric simple random walk local times converge weakly
towards a squared Bessel process. Our result can be seen as an extension of the
second Ray-Knight theorem to all asymptotically stable random walks.
