Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models

• Autores: Xia Chen
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 4, 2012, págs. 1436-1482
• Idioma: inglés
• DOI: 10.1214/11-AOP655
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• Resumen

  • Let Bs be a d-dimensional Brownian motion and ω(dx) be an independent Poisson field on Rd. The almost sure asymptotics for the logarithmic moment generating function logE0exp{±θ∫t0V¯¯¯¯(Bs)ds}(t→∞) are investigated in connection with the renormalized Poisson potential of the form V¯¯¯¯(x)=∫Rd1|y−x|p[ω(dy)−dy],x∈Rd.

    The investigation is motivated by some practical problems arising from the models of Brownian motion in random media and from the parabolic Anderson models.