Showing papers on "Subordinator published in 1995"

A new approach to the single point catalytic super-Brownian motion

Abstract: A new approach is provided to the super-Brownian motionX with a single point-catalyst δc as branching rate. We start from a superprocessU with constant branching rate and spatial motion given by the 1/2-stable subordinator. We prove that the occupation density measure λc ofX at the catalystc is distributed as the total occupation time measure ofU. Furthermore, we show thatXt is determined from λc by an explicit representation formula. Heuristically, a mass λc(ds) of “particles” leaves the catalyst at times and then evolves according to Ito's Brownian excursion measure. As a consequence of our representation formula, the density fieldx ofX satisfies the heat equation outside ofc, with a noisy boundary condition atc given by the singularly continuous random measure λc. In particular,x isC outside the catalyst. We also provide a new derivation of the singularity of the measure λc.

On the rate of growth of subordinators with slowly varying Laplace exponent

Abstract: Results of Fristedt and Pruitt [6,7] on the lower functions of a subordinator are improved in the case when the Laplace exponent is slowly varying. This yields laws of the iterated logarithm for the local times of a class of Markov processes. In particular, this extends recent results of Marcus and Rosen [9] on certain Levy processes close to a Cauchy process.

On the law of the iterated logarithm for subsequences for a stable subordinator

Abstract: Let {X(t): 0≤t<∞) be a stable subordinator with α∈(0,1). For increasing sequences tk we give normalizing constants ak such thatliminfk→∞ ak−1X(tk) is a.s constant. We also derive a.s. upper bounds.