VII: 21, 210-216, LNM 321 (1973)
MEYER, Paul-André
Note sur l'interprétation des mesures d'équilibre (
Markov processes)
Let $(X_t)$ be a transient Markov process (we omit the detailed assumptions) with a potential density $u(x,y)$. Let $\mu$ be the measure whose potential is the equilibrium potential of a set $A$. Then the distribution of the process at the last exit time from $A$ is given by $$E_x[f\circ X_{L-}, 0<L<\infty]=\int u(x,y)\,f(y)\,\mu(dy)$$ This formula, due to Chung, is deduced under minimal duality hypotheses from a general formula of Azéma, and a well-known theorem on Revuz measures
Keywords: Equilibrium potentials,
Last exit time,
Revuz measuresNature: Exposition,
Original proofs
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