2019/05/28 by Janne Junnila, Eero Saksman, Junnila, Janne +3 · 1 citation
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1905.12027
Denote by μβ="exp(βX)" the Gaussian multiplicative chaos which is defined using a log-correlated Gaussian field X on a domain U⊂ℝd. The case β∈ℝ has been studied quite intensively, and then μβ is a random measure on U. It is known that μβ can also be defined for complex values β lying in certain subdomain of ℂ, and then the realizations of μβ are random generalized functions on U. In this note we complement the results of Junnila et al. (where the case of purely imaginary β was considered) by studying the Besov-regularity of μβ and the finiteness of moments for general complex values of β.