fined on it whose finite dimensional distribution is the distribution F(atu, Ct,., Ctr) as defined above. That is, the probability structure of the stochastic process IXt, te T is completely specified by the joint distribution of F(at, It2,.,tr) for all values of T(a positive integer) and any subset(t1, t2, . tr) of T Given that, for a specific t, Xt is a random variable, we can denote its distri- bution and density function by F(at) and f(t)respectively. Moreover the mean variance and higher moments of Xt(as a r v ) can be defined as standard form E(Xt) t E(Xt-Ht)2 (at-pt)2f(ct)drt =12(t),and E(Xt) allt∈T The linear dependence measures between Xt, and Xt (t,t)=E[(X4-p1)(X12一比),t,t∈T, is now called the autocovariance function. In standardized form r(ti, ti) v(ti)u t,t;∈T is called is autocorrelation function. These numerical characteristics of the stochastic process (Xt, te T) play an important role in the analysis of the pro- cess and its application to modeling real observable phenomena. We say that {Xt,t∈T}isan process if r(ti, ti)=0 t,t;∈T,t≠t Example One of the most important example of a stochastic process is the normal process The stochastic process (Xt, tE T is said to be normal (or Gaussian) if any finite subset of T, say t1, t2, .,tr, (Xt, X,,., Xt)=x] has a multivariate normal distribution, i.e (2)-/2IVrI-1 2 exp[-(xr -Hr)V7(xr-ur)fined on it whose finite dimensional distribution is the distribution F(xt1 , xt2 , ..., xtT ) as defined above. That is, the probability structure of the stochastic process {Xt ,t ∈ T } is completely specified by the joint distribution of F(xt1 , xt2 , ..., xtT ) for all values of T (a positive integer) and any subset (t1,t2, ...,tT ) of T . Given that, for a specific t, Xt is a random variable, we can denote its distri￾bution and density function by F(xt) and f(xt) respectively. Moreover the mean, variance and higher moments of Xt (as a r.v.) can be defined as standard form as: E(Xt) = Z xt xtf(xt)dxt = µt , E(Xt − µt) 2 = Z xt (xt − µt) 2 f(xt)dxt = v 2 (t), and E(Xt) r = µrt , r ≥ 1, for all t ∈ T . The linear dependence measures between Xti and Xtj v(ti ,tj ) = E[(Xti − µti )(Xtj − µtj )], ti ,tj ∈ T , is now called the autocovariance function. In standardized form r(ti ,tj) = v(ti ,tj) v(ti)v(tj ) , ti ,tj ∈ T , is called is autocorrelation function. These numerical characteristics of the stochastic process {Xt ,t ∈ T } play an important role in the analysis of the pro￾cess and its application to modeling real observable phenomena. We say that {Xt ,t ∈ T } is an uncorrelated process if r(ti ,tj) = 0 for any ti ,tj ∈ T ,ti 6= tj . Example: One of the most important example of a stochastic process is the normal process. The stochastic process {Xt ,t ∈ T } is said to be normal (or Gaussian) if any finite subset of T , say t1,t2, ...,tT , (Xt1 , Xt2 , ..., XtT ) ≡ x 0 T has a multivariate normal distribution, i.e. f(xt1 , xt2 , ..., xtT ) = (2π) −T/2 |VT | −1/2 exp[− 1 2 (xT − µT ) 0V−1 T (xT − µT )], 3