Exit Systems and Applications
In this section we shall give several applications of the “exit system” associated with an exact terminal time. The first and most important of these is an unpublished asymptotic formula of Fitzsimmons that generalizes Spitzer’s formula [Sp64]. The nicest treatment to date of a “Spitzer’s formula” for (Borel) right processes is contained in [St87]. See also [GSt86] and [G84] for earlier versions. Exit systems are discussed in [S,§74] for a general right process X. However, there is an important simplification when X is a Borel right process. To keep the discussion as simple as possible we shall consider the case of a Borel right process first, and then indicate the extension to more general processes.
KeywordsLeft Endpoint Excessive Measure Nice Treatment Important Simplification Exit System
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