However, one should keep in mind that these properties are not necessarily limited to the finite state space case. /Matrix [1 0 0 1 0 0] Due to their good properties, they are used in various fields such as queueing theory (optimising the performance of telecommunications networks, where messages must often compete for limited resources and are queued when all ressources are already allocated), statistics (the well known “Markov Chain Monte Carlo” random variables generation technique is based on Markov chains), biology (modelling of biological populations evolution), computer science (hidden Markov models are important tools in information theory and speech recognition) and others. Starting from the mainland, what is the probability (in percentage) that the travelers will be on the mainland at the end of a 3-day trip? /Type /XObject So, a Markov chain is a discrete sequence of states, each drawn from a discrete state space (finite or not), and that follows the Markov property. /Subtype /Form S    /Subtype /Form These two quantities can be expressed the same way. Any column vector, D    H    From a theoretical point of view, it is interesting to notice that one common interpretation of the PageRank algorithm relies on the simple but fundamental mathematical notion of Markov chains. □_\square□​. Markov chains, named after Andrey Markov, are mathematical systems that hop from one "state" (a situation or set of values) to another. Once more, it expresses the fact that a stationary probability distribution doesn’t evolve through the time (as we saw that right multiplying a probability distribution by p allows to compute the probability distribution at the next time step). Reinforcement Learning Vs. *h��&�������i.�g�I.` ;�� For clarity the probabilities of each transition have not been displayed in the previous representation. 0.36 & 0.64 A Markov chain is a mathematical process that transitions from one state to another within a finite number of possible states. /Length 15 /Matrix [1 0 0 1 0 0] A Markov chain is a mathematical system that experiences transitions from one state to another according to certain probabilistic rules. A state has period k if, when leaving it, any return to that state requires a multiple of k time steps (k is the greatest common divisor of all the possible return path length). A little bit more than two decades later, Google has became a giant and, even if the algorithm has evolved a lot, the PageRank is still a “symbol” of the Google ranking algorithm (even if few people can really say the weight it still occupies in the algorithm). A Markov process is a random process for which the future (the next step) depends only on the present state; it has no memory of how the present state was reached.