We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous chaos.2010 Mathematics Subject Classification. Primary 60G15; Secondary 60G51 60F17.
We study measures associated to Brownian motions on infinitedimensional Heisenberg-like groups. In particular, we prove that the associated path space measure and heat kernel measure satisfy a strong definition of smoothness.
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