We study some remarkable path-properties of generalised stable Fleming-Viot processes (including the so-called spatial Neveu superprocess), inspired by the notion of a “wandering random measure” due to Dawson and Hochberg (1982). In particular, we make use of Donnelly and Kurtz’ (1999) modified lookdown construction to analyse their longterm scaling properties, exhibiting a rare natural example...

– We show that the nth order renormalized self-intersection local time γn(μ; t) for the symmetric stable process in R2, where the n-fold multiple points are weighted by an arbitrary measure μ, can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random measure associated with ...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields, including linear and harmonizable fractional stable fields. Almost sure and Lr-norm rates of convergenc...

This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of normalized random measures, we propose novel Markov chain Monte Carlo methods of both marginal type and conditional type. The proposed marginal samplers are ge...

The question of “levels of selection” has received a great deal of attention and controversy in the biological literature but relatively little attention in the mathematical literature. In this lecture we brie y review some background and formulate some models of multitype populations undergoing mutation and selection including multilevel selection. The main tool is a related dual processes whi...