Limit theorems for multifractal products of geometric stationary processes

作者：Denisov Denis^*; Leonenko Nikolai^*

来源：Bernoulli, 2016, 22(4): 2579-2608.

DOI：10.3150/15-BEJ738

• geometric Gaussian process
• geometric Ornstein-Uhlenbeck processes
• Levy processes
• log-gamma scenario
• log-normal scenario
• log-normal tempered stable scenario
• long-range dependence
• log-variance gamma scenario
• multifractal products
• multifractal scenarios
• Renyi function
• scaling of moments
• short-range dependence
• stationary processes
• superpositions

We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by Levy motion and their finite and infinite superpositions. We present the general conditions for the L-q convergence of cumulative processes to the limiting processes and investigate their qth order moments and Renyi functions, which are non-linear, hence displaying the multifractality of the processes as constructed. We also establish the corresponding scenarios for the limiting processes, such as log-normal, log-gamma, log-tempered stable or log-normal tempered stable scenarios.

• 出版日期2016-11