Factorization of joint multifractality

Complex systems often exhibit multifractal characteristics in various forms. The study of the joint fluctuation of multifractal objects, referred to as joint multifractality, is presented in this work. We use the joint partition function approach C. Meneveau, et al., Phys. Rev. A. 41 (1990) 894] to show that joint multifractality admits a factorization into a common factor related to the notion of relative multifractality studied by Riedi and Scheuring R.H. Riedi, I. Scheuring, Fractals 5 (1997) 153] and a remainder term related to the individual multifractality. We demonstrated our ideas using binomial measures and applied to the fluctuation of financial data.