Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes

Tutkimustuotos: Lehtiartikkelivertaisarvioitu



  • New York University


In this article we study the existence of pathwise Stieltjes integrals of the form ∫f(Xt)dYt for nonrandom, possibly discontinuous, evaluation functions f and Hölder 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(Xt) 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 large class of discontinuous evaluation functions of locally finite variation, and provide new estimates on the accuracy of numerical approximations of such integrals, together with a change of variables formula for integrals of the form ∫f(Xt)dXt.


JulkaisuStochastic Processes and their Applications
TilaSähköinen julkaisu (e-pub) ennen painettua julkistusta - 1 tammikuuta 2018
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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