Slutsky condition

Slutsky 's condition is the ergodicity condition of a random process:

A necessary and sufficient condition for ergodicity with respect to the average stationary random process with a correlation function $R_{x}$ ${\ displaystyle R_ {x}}$ $R_ {x}$ is the fulfillment of the following equality:

$\lim \limits _{T\to \infty }{1 \over T}\int \limits _{0}^{T}\!R_{x}(u)(1-{u \over T})du=0$ ${\ displaystyle \ lim \ limits _ {T \ to \ infty} {1 \ over T} \ int \ limits _ {0} ^ {T} \! R_ {x} (u) (1- {u \ over T }) du = 0}$ ${\ displaystyle \ lim \ limits _ {T \ to \ infty} {1 \ over T} \ int \ limits _ {0} ^ {T} \! R_ {x} (u) (1- {u \ over T }) du = 0}$

Named in honor of the Soviet scientist E. E. Slutsky .

Slutsky condition

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