Abstract
In this note we give an estimate of the density of a certain class of Brownian martingales in the plane, and analyze its asymptotic behaviour near the axes. In a second part, we give a result of equi-absolute continuity for the occupation measure of the Brownian martingale, and deduce the existence and uniqueness of solution for a class of hyperbolic stochastic differential equations with additive martingale noise and nondecreasing coefficient.
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