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

2005/10/26 by Bernard Roynette, Roynette, Bernard, Pierre Vallois +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60F17 #60G44 #60J25 #60J35 #60J55 #60J57 #60J60 #60J65 #AMS : 60F10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.math/0510550

openalex publication_date 2005/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Logarithmic Sobolev Inequalities

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