Penalisations of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding

• Date: 2008
• Main Authors: Roynette, B., Vallois, P., Yor, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/4558
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Penalisations of Brownian motion with its maximum and minimum processes as weak forms of Skorokhod embedding / B. Roynette, P. Vallois, M. Yor // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 2. — С. 116–138. — Бібліогр.: 25 назв.— англ.

We develop a Brownian penalisation procedure related to weight processes (Ft) of the type: Ft := f(It, St) where f is a bounded function with compact support and St (resp. It) is the one-sided maximum (resp. minimum) of the Brownian motion up to time t. Two main cases are treated: either Ft is the i...