https://insu.hal.science/insu-03606666Schmitt, F.F.SchmittMarsan, D.D.MarsanUSMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont BlancStochastic equations generating continuous multiplicative cascadesHAL CCSD200102.50.Ey05.40.FbStochastic processesRandom walks and Levy flightsCondensed Matter - Statistical MechanicsCondensed Matter - Disordered Systems and Neural Networks[SDU] Sciences of the Universe [physics]POTHIER, Nathalie2022-03-12 07:22:102022-03-13 03:26:212022-03-12 07:22:10enJournal articles10.1007/BF013139051Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the stochastic equations defining such processes, involving infinitely divisible stochastic integrals. Causal evolution laws are also given. This gives the first general stochastic equations which generate continuous multifractal measures or processes.