Contribución al estudio de la integral estocástica.
Decomposition of two parameter martingales.
In this paper we exhibit some decompositions in orthogonal stochastic integrals of two-parameter square integrable martingales adapted to a Brownian sheet which generalize the representation theorem of E. Wong and M. Zakai ([6]). Concretely, a development in a series of multiple stochastic integrals is obtained for such martingales. These results are applied for the characterization of martingales of path independent variation.
Interpolation and forecasting in Poisson's processes.
Interpolation and forecasting in Brownian functions of two parameters.
A Markov property for two parameter Gaussian processes.
This paper deals with the relationship between two-dimensional parameter Gaussian random fields verifying a particular Markov property and the solutions of stochastic differential equations. In the non Gaussian case some diffusion conditions are introduced, obtaining a backward equation for the evolution of transition probability functions.
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