A global view of Brownian penalisations

Details A global view of Brownian penalisations A global view of Brownian penalisations

2009-05-13

arxiv.org/abs/0905.2220v1

MSJ Memoirs, Mathematical Society of Japan, Volume 19, 2009

Mathematics

Probability

Scientific paper

In this monograph, we construct and study a sigma-finite measure on continuous functions from R_+ to R, strongly related to many probability measures obtained by penalisation of Brownian motion, i.e. as limits of probabilities which are absolutely continuous with respect to Wiener measure. This remarkable sigma-finite measure can be generalized in three other cases: one can start from a two-dimensional Brownian motion, from a recurrent diffusion with values in R_+, and from a discrete, recurrent Markov chain.

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