Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we… (More)

In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump… (More)

We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford’s… (More)

Members of the highly diverse bacterial phylum Verrucomicrobia are globally distributed in various terrestrial and aquatic habitats. They are key players in soils, but little is known about their… (More)

We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree… (More)

The mathematical concept of time–changing continuous–time stochastic processes can be regarded as one of the standard tools for building financial models. This article reviews briefly the theory on… (More)

Stochastic Loewner evolutions (SLE) with a multiple √ κB of Brownian motion B as driving process are random planar curves (if κ ≤ 4) or growing compact sets generated by a curve (if κ > 4). We… (More)

We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs type fragmentation tree with Aldous’s beta-splitting model, which has an extended parameter range β… (More)

We analyze the existence and properties of right inverses K for nonsymmetric Lévy processes X, extending recent work of Evans [7] in the symmetric setting. First, both X and −X have right inverses if… (More)

Abstract This article is about right inverses of Lévy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here… (More)