Dear all, I am new here and I have a mathematical question concerning fundamental geostatistical assumptions. As I see, two assumptions are usually discussed in literature. Stationarity assumption is simply expressed by
(1) E(Z(x))=m=const E(Z(x)-m)(Z(x+h)-m)=C(h) On the other hand, the intrinsic assumption is formulated as stationarity of increments Y_h(x)=Z(x+h)-Z(x) (_ denotes subscripting) which is formally expressed by (2) E(Z(x+h)-Z(x))=m_h Var(Z(x+h)-Z(x))/2=Gamma(h) (where m_h is linear in h and often considered to be 0) I can't assure myself that these formulae express the stationarity of increments Y_h. If Y_h is stationary according to (1) it is easy to derive (2). On the other hand, I can't derive stationarity of Y_h from (2). (2) can be rewritten as E(Y_h(x))=m_h Var(Y_h(x))/2=Gamma(h) The first equation correspond to the first equation of (1), but the second one states that the variance of Y_h does not depend on x, not that the covariance of Y_h does not depend on x, as requested in (1). I don't see how this can be extended. Can someone explain this? Thanks. Best regards, Mladen Nikolic ----- e-mail: niko...@matf.bg.ac.rs web: http://www.matf.bg.ac.rs/~nikolic Department of Computer Science Faculty of Mathematics University of Belgrade ----- + + To post a message to the list, send it to ai-geost...@jrc.ec.europa.eu + To unsubscribe, send email to majordomo@ jrc.ec.europa.eu with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
