Second Moment Of Customer Lifetime Value In Homogeneous Poisson Process Response

Since the1990s. Customer relationship management has been a hot issue in the marketing field. The core of customer relationship management is customer lifetime value, and it is important to clarify the probability of customer lifetime value for the relationship marketing strategy formulation.This paper focuses on the probability properties of customer lifetime value in homogeneous Poisson marketing system, such as second moment, variance and covariance. And the paper mainly includes three parts.First of all, we discuss the self-excited filtered Poisson process that response function is related to the current event and past events. And then we obtain the second moment, variance and covariance of the self-excited filtered Poisson process. Secondly, since the filtered Poisson process is a special case of the self-excited filtered Poisson process, we calculate the second moment, variance and covariance of the filtered Poisson process by using the probability properties of the self-excited filtered Poisson process.Secondly, we discuss a special kind of self-excited filtration Poisson process-the marked process of censored S shock model, and then we obtain the second moment, variance and covariance of the marked process of censored5shock model. By analyzing the marked process of censored5shock model, we find that there exists a special limit relationship between the marked process of censored8shock model and the filtered Poisson process, and then by using M function, we give a concise proof about the variance and variance of the filtered Poisson process.Finally, the marked process of censored5shock model was applied to customer lifetime value in the homogeneous Poisson process response, then we obtain the second moment, variance and covariance of customer lifetime value. The above conclusions provide a theoretical basis for the further study of marketing strategy formulation about homogeneous Poisson marketing system.In this paper, by using the analytical method, we have obtained three probability properties of customer lifetime value, which can be used for marketing decisions. This paper belongs to the phased research results that the national natural science fund project (the research on the mathematical relationship marketing based on the theory of stochastic process, number:11361049) and the science and technology plan project in Gansu province (the reliability analysis and application in relationship marketing of truncated delta shock model, number:1308RJZA147).