By the ergodic theorem, the stationary distribution is approximated by the empirical measures of the random states of the MCMC sampler.
12.
He also made many contributions to other areas including ergodic theory and he gave an elementary proof of the mean ergodic theorem.
13.
She published her thesis " Invariant measure and the ergodic theorems " in 1947 and received her Ph . D in 1948.
14.
Then the ergodic theorem is applied to transform the multi-dimensional integral to a one-dimensional integral in evaluation of the Fourier coefficients.
15.
DNA is used by researchers as a molecular tool to explore physical laws and theories, such as the ergodic theorem and the theory of elasticity.
16.
Then the pointwise ergodic theorems says that the average velocity of all particles at some given time is equal to the average velocity of one particle over time.
17.
Their first meeting, where they discussed Wiener's proof of the ergodic theorem, went so well that Pitts moved to Boston to work with Wiener.
18.
In 1927, he published his " Dynamical Systems " Birkhoff's most durable result has been his 1931 discovery of what is now called the ergodic theorem.
19.
It is a special case of the ergodic theorem where one takes the normalized angle measure \ mu = \ frac { d \ theta } { 2 \ pi }.
20.
The ergodic theorem then asserts that the average behavior of a function ? over sufficiently large time-scales is approximated by the orthogonal component of ? which is time-invariant.
