Integration formulas for Brownian motion on classical compact Lie groups

Martingale Characterizations of Stochastic Processes on Compact Groups

By a classical result of P. L evy, the Brownian motion (B t) t0 on R may be characterized as a continuous process on R such that (B t) t0 and (B 2 t ? t) t0 are martingales. Generalizations of this result are usually obtained in the setting of the so-called martingale problem. This paper contains a variant of the martingale problem for stochastic processes on locally compact groups with indepen...

Exact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries

‎In this paper Lie symmetry analysis is applied to find new‎ solution for Fokker Plank equation of geometric Brownian motion‎. This analysis classifies the solution format of the Fokker Plank‎ ‎equation‎.

Wrapping Brownian motion and heat kernels 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 the conditional transform involving the first variation

In this paper, we show that the conditional transform with respect to the Gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. We then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.