We study Atlas-type models of equity markets with local characteristics that depend on both
name and rank, and in ways that induce a stable capital distribution. Ergodic properties and …

We consider a two-dimensional semimartingale reflecting Brownian motion (SRBM) in the
nonnegative quadrant. The data of the SRBM consists of a two-dimensional drift vector, a 2× …

Given a domain G, a reflection vector field d(⋅) on ∂G, the boundary of G, and drift and
dispersion coefficients b(⋅) and σ(⋅), let L be the usual second-order elliptic operator …

Reflected Brownian motion is a continuous‐time continuous‐state Markov process, which is
constrained to its finite‐dimensional state space S by a pushing mechanism on the …

For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection
on the axes, we derive an explicit formula for the Laplace transform of its stationary …

Consider a multidimensional obliquely reflected Brownian motion in the positive orthant, or,
more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a …

We introduce a transient reflected Brownian motion in a multidimensional orthant, which is
either absorbed at the apex of the cone or escapes to infinity. We address the question of …

Brownian motion in R+ 2 with covariance matrix Σ and drift μ in the interior and reflection
matrix R from the axes is considered. The asymptotic expansion of the stationary distribution …

We consider an obliquely reflected Brownian motion Z with positive drift in a quadrant
stopped at time T, where T≔ inf {t> 0: Z (t)=(0, 0)} is the first hitting time at the origin. Such a …

We study the distribution of the supremum of the Airy process with m wanderers minus a
parabola, or equivalently the limit of the rescaled maximal height of a system of N non …