Piotr Miłoś

Inequality decomposition by population subgroups for ordinal data

We present a class of decomposable inequality indices for ordinal data (e.g. self-reported health survey). It is characterized by well-known inequality axioms (e.g. scale invariance) and a decomposability axiom which states that an index can be represented as a function of inequality values in subgroups and subgroup sizes. The only decomposable indices are strictly monotonic transformations of the weighted average of frequencies in categories. Among the indices proposed in the literature only the absolute value index (Abul Naga and Yalcin, 2008; Apouey, 2007) is decomposable. As an empirical illustration we calculate regional contributions to overall health inequality in Switzerland.

U-Statistics of Ornstein–Uhlenbeck Branching Particle System

We consider a branching particle system consisting of particles moving according to the Ornstein–Uhlenbeck process in

On truncated variation, upward truncated variation and downward truncated variation for diffusions

\mathbb {R}^d

Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment

Rd and undergoing a binary, supercritical branching with a constant rate

A note on the discrete Gaussian free field with disordered pinning on Zd, d≥2

\lambda >0

Occupation time fluctuations of Poisson and equilibrium finite variance branching systems

λ>0. This system is known to fulfill a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem (CLT) has been addressed. It turns out that the normalization and the form of the limit in the CLT fall into three qualitatively different regimes, depending on the relation between the branching intensity and the parameters of the Ornstein–Uhlenbeck process. In the present paper, we extend those results to