F(x, , Koaeees X35 tyoeees t) = {E(t,) S Kjposse5 aCe) Se 
is called the finite-dimensional distribution of the stochastic process 
E(t). For F to be a distribution, it must satisfy the following com- 
patibility conditions: 
F(x), Korres Xo CO, Ee eas tyorees t) = F(x), Koorees XS tyorees t) 
for i < n and 
F(X sees Xi Cporees t) = ape ure a8 ida abe Ea) 
where dpo---od, is an arbitrary permutation of the indicies 1, 2,..., n. 
The mean value of a stochastic process is defined by 
co 
m(t) = E[&(t)] = | x d F(x, t) 
—CO 
where E is the mathematical expected value. The mean value is thus a 
function of time. Higher moments of € are defined similarly. 
The covariance of the stochastic process is given by 
Ta (Sent) 
Covn Ge) ey ACS) 5 = SEINE) em) i CaiCs)) eer (Sy Bl 
ff (Gam Ce) es Gyan (S)) ancl ees Canyons) 
Our definition of a stochastic process is very general, and 
most systems which come under this definition would be mathematically 
unmanageable. Some specialization of the theory which makes it possible 
to characterize the distribution of E(t,), E(ty)r-++5 g(t.) in a simple 
way are particularly attractive. For instance, if the distribution of 
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