Martingale decomposition of a $L^2$ space with nonlinear stochastic integrals
Abstract
This paper presents a generalization of the KunitaWatanabe decomposition of a $L^2$ space with nonlinear stochastic integrals where the integrator is a family of continuous martingales bounded in $L^2$. To get the result, a useful relation between the regularity of the martingale family respect to its parameter and the regularity of the integrand in its martingale decomposition is shown.The decomposition presented in the main result is also the solution of an optimization problem in $L^2$. Finally, an example is given where the optimization problem is solved explicitely.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1803.00108
 Bibcode:
 2018arXiv180300108S
 Keywords:

 Mathematics  Probability;
 60G44