IV: 18, 216-239, LNM 124 (1970)
WEIL, Michel
Quasi-processus (Markov processes)
Excessive measures which are not potentials of measures were shown by Hunt (Ill. J. Math., 4, 1960) to be associated with a probabilistic object which is a kind of projective limit of Markov processes. Hunt's construction was performed in discrete time only, and is difficult in continuous time because of measure theoretic difficulties (the standard theorem on projective limits cannot be applied). Here the construction is done in full detail
Comment: Further work by M.~Weil on the same subject in 532; see the references there
Keywords: Hunt quasi-processes
Nature: Original
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V: 32, 347-361, LNM 191 (1971)
WEIL, Michel
Quasi-processus et énergie (Markov processes, Potential theory)
The energy of an excessive function $f$ with respect to an excessive measure $\xi$ has a simple proba\-bi\-listic interpretation if $\xi$ is is the potential of a measure $\mu$ and $f$ is the potential of an additive functional $(A_t)$, as ${1\over2}E_\mu[A_\infty^2]$. If $\xi$ is not a potential, still it can be associated with it a quasi-process (see Weil 418) with a birthtime $b$ and a death time $d$, and the formal expression ${1\over2}E[(A_d-A_b)^2]$ is given a precise meaning and represents the energy
Comment: This subject has been renewed by the introduction of Kuznetsov's measures. See Fitzsimmons Sem. Stoch. Proc., 1987
Keywords: Hunt quasi-processes, Energy
Nature: Original
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