# 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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