Brownian Processes for Monte Carlo Integration on Compact Lie Groups

Brownian Processes for Monte Carlo Integration on Compact Lie Groups

This paper proposes a Monte Carlo approach for the evaluation of integrals of smooth functions defined on compact Lie groups. The approach is based on the ergodic property of Brownian processes in compact Lie groups. The paper provides an elementary proof of this property and obtains the following results. It gives the rate of almost sure convergence of time averages along with a “large deviati...

Integration formulas for Brownian motion on classical compact Lie groups

Combinatorial formulas for the moments of the Brownian motion on classical compact Lie groups are obtained. These expressions are deformations of formulas of B. Collins and P. Śniady for moments of the Haar measure and yield a proof of the First Fundamental Theorem of Invariant and of classical Schur-Weyl dualities based on stochastic calculus.

Monte Carlo Filtering on Lie Groups

We propose a nonlinear lter for estimating the trajectory of a random walk on a matrix Lie group with constant computational complexity. It is based on a nite-dimensional approximation of the conditional distribution of the state given past measurements via a set of fair samples, which are updated at each step and proven to be consistent with the updated conditional distribution. The algorithm ...

Wrapping Brownian motion and heat kernels on compact Lie groups

Probability on Compact Lie Groups