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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 14, Fasc. 1,
pages 33 - 44
 

STOCHASTIC PROCESSES WITH LINEAR CONDITIONAL EXPECTATION AND QUADRATIC CONDITIONAL VARIANCE

Jacek Wesołowski

Abstract: Linear conditional expectations and quadratic conditional variances determine a class of stochastic processes with independent increments. Characterizations of the Wiener, Poisson, gamma, negative binomial and hyperbolic secant processes are obtained. Also a result on existence and determination of moments by the first two conditional moments for a sequence of random variables is proved.

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

Key words and phrases: -

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