Collision Local Times and Measure-Valued Processes

  title={Collision Local Times and Measure-Valued Processes},
  author={Martin T. Barlow and Steven N. Evans and Edwin A. Perkins},
We consider two independent Dawson-Watanabe super-Brownian motions, Y' and y2. These processes are diffusions taking values in the space of finite measures on Rd. We show that if d < 5 then with positive probability there exist times t such that the closed supports of Ytl and t2 intersect; whereas if d > 5 then no such intersections occur. For the case d < 5, we construct a continuous, non-decreasing measure-valued process L(Yl,Y2), the "collision local time", such that the measure defined by… CONTINUE READING