Stationary measures for certain stochastic processes

The Existence Op Stationary Measures for Certain Markov 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(...

Srb Measures for Certain Markov Processes

We study Markov processes generated by iterated function systems (IFS). The constituent maps of the IFS are monotonic transformations of the interval with common fixed points at 0 and 1. We first obtain an upper bound on the number of SRB (Sinai-Ruelle-Bowen) measures for the IFS. Then theorems are given to analyze properties of the ergodic invariant measures δ0 and δ1. In particular, sufficien...

Quasi-stationary Measures for Discrete-state Markov Processes Where Absorption May Not Be Certain

Prediction for Non-Stationary Stochastic Processes – II

A method is presented for extrapolation of time-series which contain time-varying frequency components. The time-series is complex-demodulated at a set of frequencies. The resulting time-frequency time-series are assumed to be time-dependent such that the amplitude and phase change relatively slowly with time. This change is taken into account in the extrapolation. This model of a non-stationar...