P\'{e}nalisations of Walsh's Brownian motion

Publication date: 16 June 2005

Abstract: In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to infinity, and we study the behaviour of this limit measure.

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Brownian motion (60J65) Martingales with continuous parameter (60G44) Sample path properties (60G17) Convergence of probability measures (60B10) Local time and additive functionals (60J55)

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