Analysis of complex Brownian motion

Brownian Motion: The Link Between Probability and Mathematical Analysis

This article has no abstract.

Brownian motion, complex analysis, and the dimension of the Brownian frontier

Analysis of Complex Brownian Functionals

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...

Principal Component Analysis of Fractional Brownian Motion

This paper gives an analytical proof of the conjecture [1]: when the dimension M of the auto-covariance matrix is large, the eigenvalue spectrum from Principal Component Analysis (PCA) of a fractal Brownian motion (fBm) process with Hurst parameter H decays as a power-law: λm ∼ m −(2H+1), m = 1,..., M . This resolves the interesting puzzle why PCA based H estimator can yield right results for f...