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Is IID a Markov chain?
Any iid sequence forms a Markov chain, for if {Xn} is iid, then {Xn+1,Xn+2,…} In fact {Xn+1,Xn+2,…} is independent of {X0,…,Xn} (the past and the present): For an iid sequence, the future is independent of the past and the present state.
What are the different states of Markov chain?
A Markov chain with one transient state and two recurrent states A stochastic process contains states that may be either transient or recurrent; transience and recurrence describe the likelihood of a process beginning in some state of returning to that particular state.
What is Markov chains used for?
Markov Chains are exceptionally useful in order to model a discrete-time, discrete space Stochastic Process of various domains like Finance (stock price movement), NLP Algorithms (Finite State Transducers, Hidden Markov Model for POS Tagging), or even in Engineering Physics (Brownian motion).
What are the properties of a Markov chain?
Properties of Markov Chains: Reducibility. Markov chain has Irreducible property if it has the possibility to transit from one state to another. Periodicity. If a state P has period R if a return to state P has to occur in R multiple ways. Transience and recurrence. Ergodicity.
How does a Markov chain work?
A Markov chain is a mathematical system that experiences transitions from one state to another according to certain probabilistic rules. The defining characteristic of a Markov chain is that no matter how the process arrived at its present state, the possible future states are fixed.
What is a homogeneous Markov chain?
I learned that a Markov chain is a graph that describes how the state changes over time, and a homogeneous Markov chain is such a graph that its system dynamic doesn’t change. Here the system dynamic is something also called transition kernel which means the calculation of the probability from one station to the next station.
What is Markov chain applications?
It is named after the Russian mathematician Andrey Markov . Markov chains have many applications as statistical models of real-world processes , such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics.