Lévy Processes

Lévy processes are random processes on Euclidean space that are stochastically continuous and have stationary independent increments. They, and their stochastic integrals, have become useful tools in a variety of nonparametric statistical and environmetric applications including density estimation, survival analysis, regression, and spatial modeling. At times we may be willing to assume that some observed random lifetimes Ti come from a particular parametric family of distributions, like the Weibull or lognormal or gamma families, so that inference about their distribution reduces to the problem of estimating parameters. In some other problems, especially those in which we fear that the actual distribution has features like multi-modality, heavy tails, etc. that make the commonly-used distributions inappropriate, we may prefer to use a nonparametric modeling approach in which the survival function