Johanna GarzónJorge A. LeónTorres, SoledadSoledadTorres2025-12-082025-12-082023-08-0110.3150/22-bej15242-s2.0-85159845977https://cris-uv-2.scimago.es/handle/123456789/7998WOS:001005621300005In this article, we study the forward integral, in the Russo and Vallois sense, with respect to Hölder continuous stochastic processes Y with exponent bigger than 1/2. Here, the integrands have the form f (Y), where f is a bounded variation function. As a consequence of our results, we show that this integral agrees with the generalized Stieltjes integral given by Zähle and that, in the case that Y is fractional Brownian motion, this forward integral is equal to the divergence operator plus a trace term, which is related to the local time of Y. Moreover, the definition of the forward integral allows us to obtain a representation of the solutions to forward stochastic differential equations with a possibly discontinuous coefficient and, as a consequence of our analysis, to figure out some explicit solutions.enacceso restringidoStatistics And Probabilityarticle