Local Times and Excursion Theory for Brownian Motion by Ju-Yi Yen & Marc Yor

Author:Ju-Yi Yen & Marc Yor
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

We discuss two disintegrations of the Itô measure n, respectively in terms of the lifetime V and the maximum M.

This chapter, and more generally, all discussions pertaining to excursion theory, is a condensed version of Chap. XII in Revuz–Yor [2], where the reader shall find more details.

6.1 Statements

The next two descriptions of n are extremely useful. Their importance justifies that we put them in boxes:

(1)(Itô’s representation of n)

Conditioning with respect to the lifetime V. (a)The “law” of V under n is:

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