scholarly journals Some remarks on Pitman’s theorem

1997 ◽  
pp. 266-271 ◽  
Author(s):  
Bernhard Rauscher
Keyword(s):  
Pitman’S Theorem

scholarly journals Some extensions of Pitman and Ray-Knight theorems for penalized Brownian motions and their local times, IV

2007 ◽  
Vol 44 (4) ◽  
pp. 469-516 ◽  
Author(s):  
Bernard Roynette ◽  
Pierre Vallois ◽  
Marc Yor
Keyword(s):  
Brownian Motion ◽  
Local Times ◽  
Brownian Motions ◽  
Pitman’S Theorem

We show that Pitman’s theorem relating Brownian motion and the BES (3) process, as well as the Ray-Knight theorems for Brownian local times remain valid, mutatis mutandis, under the limiting laws of Brownian motion penalized by a function of its one-sided maximum.

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