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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 measures

Nature: Exposition, Original proofs

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XIV: 44, 418-436, LNM 784 (1980)

**RAO, Murali**

A note on Revuz measure (Markov processes, Potential theory)

The problem is to weaken the hypotheses of Chung (*Ann. Inst. Fourier,* **23**, 1973) implying the representation of the equilibrium potential of a compact set as a Green potential. To this order, Revuz measure techniques are used, and interesting auxiliary results are proved concerning the Revuz measures of natural additive functionals of a Hunt process

Keywords: Revuz measures, Additive functionals, Hunt processes, Equilibrium potentials

Nature: Original

Retrieve article from Numdam

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 measures

Nature: Exposition, Original proofs

Retrieve article from Numdam

XIV: 44, 418-436, LNM 784 (1980)

A note on Revuz measure (Markov processes, Potential theory)

The problem is to weaken the hypotheses of Chung (

Keywords: Revuz measures, Additive functionals, Hunt processes, Equilibrium potentials

Nature: Original

Retrieve article from Numdam