CHARACTERIZATIONS OF POLYNOMIAL-GAUSSIAN PROCESSES THAT
ARE MARKOVIAN

Abstract: We consider questions of characterizing a stochastic process
by the properties of the first two conditional moments. Our first result is a
new version of the classical P. Lévy characterization theorem for martingales. Next we deal
with a characterization of processes without continuous trajectories. We consider a special
form of the initial state. Namely, we suppose that the r.v. has a polynomial-normal
distribution (PND), i.e. the density of is the product of a positive polynomial and a
normal density.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -