  We generalize the notion of renormalized solution to semilinear elliptic and
parabolic equations involving operator associated with general (possibly
nonlocal) regular Dirichlet form and smooth measure on the right-hand side. We
show that under mild integrability assumption on the data a quasi-continuous
function $u$ is a renormalized solution to an elliptic (or parabolic) equation
in the sense of our definition iff $u$ is its probabilistic solution, i.e. $u$
can be represented by a suitable nonlinear Feynman-Kac formula. This implies in
particular that for a broad class of local and nonlocal semilinear equations
there exists a unique renormalized solution.
