Martingale limit theorems of divisible statistics in a multinomial scheme with mixed frequencies

The martingale approach to limit theorems of divisible statistics in non-classical multinomial schemes, established by Khmaladze in 1983, has shown great power for those models with all asymptotically Poissonian frequencies. We extended this approach to more general situations, which include both asymptotically Gaussian and Poissonian frequencies, and established functional limit theorems.