The Concave Majorant of Brownian Motion

The Concave Majorant of Brownian Motion

The distribution of the maximal difference between Brownian bridge and its concave majorant

We provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this difference. This maximal difference has an application in nonparametric statistics where it arises in testing monotonicity of a density or regression curve.

Brownian Motion: The Link Between Probability and Mathematical Analysis

This article has no abstract.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Brownian Brownian Motion – I

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M ≫ 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of...