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.

Additional Metadata
Keywords Continuity and regularity of stochastic processes, Fluctuation limits, Sobolev spaces, Stochastic partial differential equations
Persistent URL dx.doi.org/10.1080/07362994.2012.727137
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