Bridge Simulation and Metric Estimation on Lie Groups

Mathias H{\o}jgaard Jensen; Sarang Joshi; Stefan Sommer

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Bridge Simulation and Metric Estimation on Lie Groups

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arxiv 2106.03431 v1 pith:BX3KYPCR submitted 2021-06-07 math.ST math.PRstat.COstat.TH

Mathias H{o}jgaard Jensen , Sarang Joshi , Stefan Sommer This is my paper

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keywords groupssimulationbridgebrownianguidedmeasuremetricprocess

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abstract

We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group $\SO(3)$. In particular, we apply importance sampling to estimate the metric on $\SO(3)$ using an iterative maximum likelihood method.

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