The Markov chain of Hidden Markov Model of interaction of the K-RAS4B proteins in catalytic environment with lipid membranes has a Hilbert measure

A Hidden Markov Model containing both stationary Markov processes and time-varyingMarkovprocessesisconsidered: thecorrespondingMarkovchainisnewly proven to be one whose transition operators are on a space with Hilbert metric (whose measure exists and is unique). The Markov chain is therefore newly proven to be one with bounded moments. The further mathematical developments are envisaged. Applications are newly given for the analytical expressions of description of allosteric systems. The model of interaction of the K-RAS4B proteins with lipid membranes is newly considered accordingly; new drug design is explained