Stochastic Calculus of Variations on complex line bundle and construction of unitarizing measures for the Poincare disk

摘要

Holomorphic representation of Lie algebra can be realized through Kahlerian symplectic formalism; underlying holomorphic convexity requires then the introduction of elliptic operators with complex coefficients. We construct the Stochastic Calculus of Variations for those elliptic operators; remote past vanishing of projections or the underlying process implies convergence in law; then limit laws lead to the unitarizing measure of the given representation; this general approach is developed in full details on Poincare disk. (C) 2008 Elsevier Inc. All rights reserved.