A functional Itō-formula for Dawson–Watanabe superprocesses

Conditional Excursion Representation for a Class of Interacting Superprocesses

A class of interacting superprocesses, called superprocesses with dependent spatial motion (SDSMs), has been introduced and characterized in Wang [22] and Dawson et al. [7]. In this paper, we give a construction or an excursion representation of the non-degenerate SDSM with immigration by making use of a Poisson system associated with the conditional excursion laws of the SDSM. As pointed out i...

Brownian bugs and superprocesses

Advection-diffusion-reaction (adr) models link physical oceanography and biological oceanography. These models, which describe biology using continuous concentration fields, usually neglect individual-scale fluctuations. I describe a stochastic individual-based model, called the Brownian bug process, which illustrates some of the surprising issues associated with the neglect of fluctuations by ...

A Functional Description of TEX's Formula Layout

While the quality of the results of T E X's mathematical formula layout algorithm is convincing, its original description is hard to understand since it is presented as an imperative program with complex control ow and destructive manipulations of the data structures representing formulae. In this paper, we present a re-implementation of T E X's formula layout algorithm in the functional langua...

Interacting Superprocesses and Conditional Independence

Non-linear superprocesses

Non-linear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the non-linear martingale problems under Lipschitz conditions on the coe cients. Mathematics Subject Classi cation (1991): 60G57, 60K35, 60J80.