We prove the existence and uniqueness of a local solution for stochastic differential equations in the plane with local Lipschitz coefficients, and state the existence of random points where the solution explodes. A sufficient condition to obtain a global solution is given.

We study the existence and properties of the density for the law of the solution to a nonlinear hyperbolic stochastic partial differential equation, driven by a two-parameter white noise. We also analyze the asymptotic behavior of the density for the law of the solution to the equation obtained...

We study the Euler approximation scheme for solutions of stochastic differential equations with boundary conditions in two different examples: (a) the one-dimensional case with linear boundary condition, and (b) the multidimensional case with constant diffusion coefficient and general boundary...

In this paper we state Green type formulas for nonadapted processes with respect to "anticipating semimartingales", say U, in the Stratonovich and the Skorohod formulation. To this end we develop some notions of anticipating stochastic calculus with respect to U, based on multiple and line...