Titlebook: Local Times and Excursion Theory for Brownian Motion; A Tale of Wiener and Ju-Yi Yen,Marc Yor Book 2013 Springer International Publishing S

拱形面包

Local Times and Excursion Theory for Brownian MotionA Tale of Wiener and

不自然

Lévy’s Representation of Reflecting BM and Pitman’s Representation of BES(3)ubtracts Brownian motion from twice its one sided supremum, the obtained process is distributed as a BES(3) process. Extensions of these theorems to Brownian motion with drift are shown. The Azéma–Yor explicit solution to Skorokhod’s embedding problem is shown; it involves a first hitting time by Brownian motion and its one-sided supremum.

affluent

Yourself

Brownian Excursion Theory: A First Approachicative one, are proven. They allow to compute expectations of sums or products of excursion functionals in terms of .. The Lévy measures of Brownian additive functionals, considered at inverse local time are shown to be expressible in terms of .. The distributions of the lifetime and the maximum of the generic excursion under . are computed.

哺乳动物

A Simple Path Decomposition of Brownian Motion Around Time , = 1Brownian bridge, the BES(3) bridge, and the Brownian meander. Independence properties of the Brownian meander allow to study Azéma’s remarkable martingale, which enjoys the chaos representation property, as shown by Emery.

混沌

Ancillary

Integral Representations Relating W and nrse local time integral of Wiener measure and the level integral of Wiener measure up to first hit of 0 by Brownian motion, or last passage time at a level by the BES(3) process. These relations shall play a key role in our derivation of the Feynman–Kac formula in the next chapter.