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Journal Articles J. Math. Soc. Japan Year : 2019

Local time penalizations with various clocks for one-dimensional diffusions

Abstract

For a generalized one-dimensional diffusion, we consider the measure weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times, which we will call a clock. The aim is to give a systematic study of the penalization with the clock, i.e., its limit as the clock tends to infinity. We also discuss universal σ-finite measures which govern certain classes of penalizations, thus giving a path interpretation of these penalized processes.
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Dates and versions

hal-01358615 , version 1 (01-09-2016)

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Christophe Profeta, Kouji Yano, Yuko Yano. Local time penalizations with various clocks for one-dimensional diffusions. J. Math. Soc. Japan, 2019, 71 (1), pp.203-233. ⟨hal-01358615⟩
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