@article{EJP27,
author = {Steven Evans and Edwin Perkins},
title = {Collision Local Times, Historical Stochastic Calculus, and Competing Species},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {3},
year = {1998},
keywords = {super-process, super-Brownian motion, interaction, local time, historical process, measure-valued Markov branching process, stochastic calculus, martingale measure, random measure},
abstract = {Branching measure-valued diffusion models are investigated that can be regarded as pairs of historical Brownian motions modified by a competitive interaction mechanism under which individuals from each population have their longevity or fertility adversely affected by collisions with individuals from the other population. For 3 or fewer spatial dimensions, such processes are constructed using a new fixed-point technique as the unique solution of a strong equation driven by another pair of more explicitly constructible measure-valued diffusions. This existence and uniqueness is used to establish well-posedness of the related martingale problem and hence the strong Markov property for solutions. Previous work of the authors has shown that in 4 or more dimensions models with the analogous definition do not exist.},
pages = {no. 5, 1-120},
issn = {1083-6489},
doi = {10.1214/EJP.v3-27},
url = {http://ejp.ejpecp.org/article/view/27}}