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}
}
  • Clarence Simard
  • Published 28 February 2018
  • Mathematics, Computer Science
  • Journal of Applied Probability
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… Expand

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TLDR
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