We obtain high-density fluctuation limits for trajectories of the motions in Cox systems of independent motions in "Rd". The motions are quite general; they include a large class of diffusions, Brownmian bridges and fractional Brownian motions. The limits take values ina space of distributions...

We constructs a class of seperprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitary bounded non-negative Borel...

We introduce adapted sets and optional sets and we study a type of strong Markov property for set-indexed precesses, that can be associated with the sharp Markov property defined by Ivanoff and Merzbach (2000a).

We propose a Poisson modelling approach to random effects Cox proportional hazards models. Specifically we describe methods of statistical inference for a class of random effects Cox models which accommodate a wide range of nested random effects distributions. The orthodox BLUP approach to...

We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 < < 1, uniform Poisson initial state) in the case of intermediate dimensions, / < d < (1 + )/. The limit is a process of the form K, where K is a constant, is the Lebesgue measure on Rd, and = (t)t0 is a (1+)-stable process which has long range dependence. There are two long range dependence regimes, one for all > d/(d + ), which coincides with...</<>