Multifractal random walk - art. no. 026103

We introduce a class of multifractal processes, referred to as multifractal random walks (MRWs). To our knowledge, it is the first multifractal proces s with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascadelike mu ltifractal models since they do not involve any particular scale ratio. The MRWs are indexed by four parameters that are shown to control in a very di rect way the multifractal spectrum and the correlation structure of the inc rements. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.