Brownian motion with singular drift

• Richard F. Bass ^[1] ; Zhen-Qing Chen ^[2]
  1. [1] University of Connecticut

     University of Connecticut

     Town of Mansfield, Estados Unidos

     
  2. [2] University of Washington

     University of Washington

     Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 2, 2003, págs. 791-817
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider the stochastic differential equation dXt=dWt+dAt, where Wt is d-dimensional Brownian motion with d≥2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure πi as ∫t0f(Xs)ds does to the measure f(x)dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures πi are members of the Kato class \Kd−1. As a typical example, we obtain a Brownian motion that has upward drift when in certain fractal-like sets and show that such a process is unique in law.