Homeomorphism of the Revuz correspondence for finite energy integrals

Takumu Ooi

Stochastic Processes and their Applications, 2026, vol. 191, issue C

Abstract: We provide necessary and sufficient conditions for the convergence of Revuz measures of finite energy integrals. More precisely, the Revuz map from the set of all smooth measures of finite energy integrals, equipped with the topology induced by the norm given by the sum of the Dirichlet form and the L2(m)-norm, to the space of positive continuous additive functionals, equipped with the topology induced by the L2(Pm+κ+ν0)-norm with the local uniform topology, is a homeomorphism, where m is the underlying measure, κ is the killing measure of a Dirichlet form and ν0 is an energy functional corresponding to the part of the process that continuously escapes to the cemetery point.

Keywords: Dirichlet form; Revuz measure; Positive continuous additive functional (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104787

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