Excursion Theory Revisited
Excursion Theory Revisited
P.J. Fitzsimmons and R.K. Getoor
Excursions from a fixed point b are studied in the
framework of a general Borel right process X, with a fixed excessive
measure m serving as background measure; such a measure always exists
if b is accessible from every point of the state space of X. In this
context the left-continuous moderate Markov dual process
Xhat arises naturally and plays an important role. This allows
the basic quantities of excursion theory such as the Laplace-Lévy
exponent of the inverse local time at b and the Laplace transform of
the entrance law for the excursion process to be expressed as inner
products involving simple hitting probabilities and expectations. In
particular if X and
Xhat are honest, then the resolvent of X may be expressed
entirely in terms of quantities that depend only on X and
Xhat killed when they first hit b.
A hard copy of this manuscript is available from the
first-named author upon request.
The manuscript can also be downloaded in
dvi form (216K),
postscript form (764K),
and pdf form (637K).
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May 10, 2005
