Limiting laws associated with Brownian motion perturbated by normalized exponential weights I

Details Limiting laws associated with Brownian motion perturbated by normalized exponential weights I Limiting laws associated with Brownian motion perturbated by normalized exponential weights I

2005-10-26

arxiv.org/abs/math/0510550v1

Mathematics

Probability

Scientific paper

We determine the rate of decay of the expectation Z(t) of some multiplicative
functional related to Brownian motion up to time t. This permits to prove that
the Wiener measure, penalized by this multiplicative functional, converges as t
goes to infinity to a probability measure (p.m.) . We obtain the law of the
canonical process under this new p.m.

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