Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes

@article{Chen2016PathwiseSI,
  title={Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes},
  author={Zhe Chen and Lasse Leskela and Lauri Viitasaari},
  journal={Stochastic Processes and their Applications},
  year={2016},
  volume={129},
  pages={2723-2757}
}
Abstract In this article we study the existence of pathwise Stieltjes integrals of the form ∫ f ( X t ) d Y t for nonrandom, possibly discontinuous, evaluation functions f and Holder continuous random processes X and Y . We discuss a notion of sufficient variability for the process X which ensures that the paths of the composite process t ↦ f ( X t ) are almost surely regular enough to be integrable. We show that the pathwise integral can be defined as a limit of Riemann–Stieltjes sums for a… Expand
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