Torres, SoledadSoledadTorresCiprian A. Tudor2025-12-062025-12-062016-09-2410.1007/s10959-016-0713-52-s2.0-84991401472https://cris-uv-2.scimago.es/handle/123456789/6985WOS:000426359200015We define a multifractal random walk (MRW) as an anticipating pathwise integral, as limit of Riemann sums. The MRW is usually defined as the limit as r→ 0 of the family of stochastic processes (Xr)rCloseSPigtSPi0 where (Formula presented.) Xr(t)=∫0tQr(u)dW(u),t≥0,where W is a Wiener process and Q an infinitely divisible cascading noise (IDC noise) not adapted to the filtration generated by W. In order to define the stochastic integral Xr(t) and to simulate it, one usually assumes that Q and W are independent. Our purpose is to define the MRW with a dependence structure between the IDC noise Q and the Wiener process W. Our construction is done by using Riemann sums, and it allows the simulation of the process.enacceso restringidoMathematicsStatistics And ProbabilityStatistics, Probability And Uncertaintyarticle