Local conditioning in Dawson–Watanabe superprocesses

Local Conditioning in Bayesian Networks

Local conditioning (LC) is an exact algorithm for computing probability in Bayesian networks, developed as an extension of Kim and Pearl’s algorithm for singly-connected networks. A list of variables associated to each node guarantees that only the nodes inside a loop are conditioned on the variable which breaks it. The main advantage of this algorithm is that it computes the probability direct...

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

Optimal local Hölder index for density states of superprocesses with 1+-branching mechanism

Received May 2008; revised April 2009. Supported by the German Israeli Foundation for Scientific Research and Development, Grant G-807-227.6/2003. AMS 2000 subject classifications. Primary 60J80; secondary 60G57.

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.