Martingale characterization of Pólya processes and sequences
В. В. Некруткин · Vestnik St Petersburg University Mathematics · 2007
It is proved that a mixed Poisson process ξ t is a Pólya process if and only if there exists a nondegenerate linear transform ξ t → η t = a ( t )ξ t + b ( t ) such that η t is a martingale. A similar result is valid for Pólya sequences.