STOCHASTIC PROCESSES WITH LINEAR CONDITIONAL
EXPECTATION AND QUADRATIC CONDITIONAL VARIANCE
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: -