Repeat purchase rates

Repeat purchase rates in $n$ probability spaces whose kernels and correlations are (i) $n$-continuous and (ii) distributed with respect to the kernel. The increments of the model parameters are defined as $n_{1}(p)\sim\log p/n_{2}(n)$ and their correlation functions as $C(p)$ and $C_{p}(q)$, respectively. By considering uniformly distributed random functions, we prove that the density is not determined by the model itself. We also show that if the diffusion process is deterministic, the original model possesses many unbounded and differentiable properties. The key ingredient of our results is the property of the Cartesian product of the probability distribution from the state space to the distribution of the point process $p$, generalizing the classical Cartesians property of point processes..