Subadditive stochastic processes

Kingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

Subadditive Ergodic Theorems

Above is the famous Fekete’s lemma which demonstrates that the ratio of subadditive sequence (an) to n tends to a limit as n approaches infinity. This lemma is quite crucial in the field of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting. Kingman’s Subadditive Ergodic ...

Stochastic Processes

Stochastic Processes

Stochastic Processes ( Fall 2014 ) Spectral representations and ergodic theorems for stationary stochastic processes Stationary stochastic processes

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...