Explicit solution of the general multitype Lamperti representation

Construct an explicit expression for the pathwise solution of the multitype Lamperti stochastic differential equation as a function of the driving Lévy processes in dimensions beyond the one-type case and beyond the 2-cyclic two-type case.

Background

A Lamperti representation for multitype branching processes expresses each component of the process through Lévy processes evaluated at integrated population times. Although existence and pathwise uniqueness are known, an explicit representation of the solution in terms of the driving Lévy processes is generally unavailable.

The paper derives such an expression in the 2-cyclic two-type configuration. The corresponding problem for general multitype branching processes remains unresolved.