Summary
LetX be a BES0(d) (0<d<1) with canonical decompositionX=B+(d−1)H, whereB is a brownian motion andH locally of zero energy. The process (X; H) is shown to have a local time at (0; 0), and the characteristic measure of its excursions (in Itô's sense) is described. This study leads us to new determinations of the-space variable-process defined by the occupation densities ofH taken at some optional times.
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Bertoin, J. Excursions of a BES0 (d) and its drift term (0<d<1). Probab. Th. Rel. Fields 84, 231–250 (1990). https://doi.org/10.1007/BF01197846
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DOI: https://doi.org/10.1007/BF01197846