Weak Convergence of Interacting SDEs to the Superprocess

Applied Mathematics & Optimization - Tập 41 - Trang 111-128 - 2000
A. Bose1, P. Sundar2
1Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada , , CA
2Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, USA, , US

Tóm tắt

A finite system of stochastic differential equations defined on a lattice with nearest-neighbor interaction is scaled so that the distance between lattice sites decreases and the size of the system increases. The space—time process defined by the above system is shown to converge in law to the solution of the SPDE associated with the super-Brownian motion on [0, 1] .