# Martingale decomposition of an L2 space with nonlinear stochastic integrals

@article{Simard2019MartingaleDO, title={Martingale decomposition of an L2 space with nonlinear stochastic integrals}, author={Clarence Simard}, journal={Journal of Applied Probability}, year={2019}, volume={56}, pages={1231 - 1243} }

Abstract This paper generalizes the Kunita–Watanabe decomposition of an
$L^2$
space. The generalization comes from using nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in
$L^2$
. This result is also the solution of an optimization problem in
$L^2$
. First, martingales are assumed to be stochastic integrals. Then, to get the general result, it is shown that the regularity of the family of martingales with respect to its spatial parameter…

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