Williams decomposition for superprocesses

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 ...

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.

Multitasking: Optimal Planning for Bandit Superprocesses

A bandit superprocess is a decision problem composed from multiple independent Markov decision processes (MDPs), coupled only by the constraint that, at each time step, the agent may act in only one of the MDPs. Multitasking problems of this kind are ubiquitous in the real world, yet very little is known about them from a computational viewpoint, beyond the observation that optimal policies for...

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...