  By considering special sampling of discrete scale invariant (DSI) processes
we provide a sequence which is in correspondence to multi-dimensional
self-similar process. By imposing Markov property we show that the covariance
functions of such discrete scale invariant Markov (DSIM) sequences are
characterized by variance, and covariance of adjacent samples in the first
scale interval. We also provide a theoretical method for estimating spectral
density matrix of corresponding multi-dimensional self-similar Markov process.
Some examples such as simple Brownian motion with drift and scale invariant
autoregressive model of order one are presented and these properties are
investigated. By simulating DSIM sequences we provide visualization of their
behavior and investigate these results. Finally we present a new method to
estimate Hurst parameter of DSI processes and show that it has much better
performance than maximum likelihood method for simulated data.
