Abstract: In this paper it is shown that the equilibrium measure for a compact in potential
theory can be related with a unique invariant measure for a discrete time Markov
process by the formula The chain has the transition function
where is the last-exit kernel in [1]. For a general non-symmetric potential
density u the modified energy and the Gauss
quadratic are introduced. Then is minimized by
among all signed measures on of finite modified energy, provided is
positive. This includes the classical symmetric case of Newtonian and M. Riesz
potentials as a special case. The modification corresponds to a time change for
the underlying Markov process. The positivity of is established for a class of
signed measures associated with continuous additive functionals in the sense of
Revuz.
for a compact 
in potential
theory can be related with a unique invariant measure 
for a discrete time Markov
process by the formula 
The chain has the transition function
where 
is the last-exit kernel in [1]. For a general non-symmetric potential
density u the modified energy 
and the Gauss
quadratic 
are introduced. Then 
is minimized by 
among all signed measures 
on 
of finite modified energy, provided 
is
positive. This includes the classical symmetric case of Newtonian and M. Riesz
potentials as a special case. The modification corresponds to a time change for
the underlying Markov process. The positivity of 
is established for a class of
signed measures associated with continuous additive functionals in the sense of
Revuz.