A Class of Affine Processes Arising as Fluctuation Limits of Super-Brownian Motion in a Super-Brownian Catalytic Medium
A class of infinite dimensional Ornstein-Uhlenbeck processes that arise as solutions of stochastic partial differential equations with noise generated by measure-valued catalytic processes is investigated. It will be shown that the catalytic Ornstein-Uhlenbeck process with super-Brownian catalyst in one dimension arises as a high density fluctuation limit of a super-Brownian motion in a super-Brownian catalyst with immigration. The main tools include Laplace transformations of stochastic processes, analysis of a non-linear partial differential equation and techniques on continuity and regularity based on properties of the Sobolev spaces.
|Keywords||Continuity and regularity of stochastic processes, Fluctuation limits, Sobolev spaces, Stochastic partial differential equations|
|Journal||Stochastic Analysis and Applications|
Perez-Abarca, J.-M. (Juan-Manuel), & Dawson, D.A. (2012). A Class of Affine Processes Arising as Fluctuation Limits of Super-Brownian Motion in a Super-Brownian Catalytic Medium. Stochastic Analysis and Applications, 30(6), 1041–1061. doi:10.1080/07362994.2012.727137