Cameron--Martin formula for the σ-finite measure unifying Brownian penalisations

2009/09/28 by Kouji Yano, Yano, Kouji
Mathematics · #46G12 #60H05 #60J65 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR #msc:46G12 #msc:60H05 #msc:60J65

paper · pdf · doi:10.48550/arxiv.0909.5132

arxiv created 2009/11/10 · arxiv updated 2009/12/01

Abstract

Quasi-invariance under translation is established for the σ-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor. For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor, plays a key role.

Related

• Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations
• Cameron--Martin Type Theorem for a Class of non-Gaussian Measures
• Integration by parts on the law of the reflecting Brownian motion
• On a Cameron--Martin Type Quasi-Invariance Theorem and Applications to Subordinate Brownian Motion
• On sigma-finite measures related to the Martin boundary of recurrent Markov chains