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Contents of PMS, Vol. 23, Fasc. 1,
pages 7 - 18
 

CHARACTERIZATIONS OF POLYNOMIAL-GAUSSIAN PROCESSES THAT ARE MARKOVIAN

Agnieszka Plucińska

Abstract: We consider questions of characterizing a stochastic process X = (X ,t > 0) t 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. X 0 has a polynomial-normal distribution (PND), i.e. the density of X 0 is the product of a positive polynomial and a normal density.

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

Key words and phrases: -

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