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Is this a regular Markov chain?
A transition matrix P is regular if some power of P has only positive entries. A Markov chain is a regular Markov chain if its transition matrix is regular. For example, if you take successive powers of the matrix D, the entries of D will always be positive (or so it appears). So D would be regular.
What makes something a Markov chain?
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 the purpose of Markov chain?
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).
Can you model a Poisson process as a Markov process?
You can model a Poisson Process as a Markov Process: its just a pure-birth chain. So, Poisson process is a type of Markov process. However, there are some Markov Processes that are bounded/finite state space. For example, you want to model the weather with choices $\\{rainy, sunny, cloudy\\}$.
Which is the correct definition of a Markov chain?
For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space).
Is there such a thing as a continuous time Markov chain?
Usually the term “Markov chain” is reserved for a process with a discrete set of times, that is, a discrete-time Markov chain (DTMC), but a few authors use the term “Markov process” to refer to a continuous-time Markov chain (CTMC) without explicit mention.
When does a stochastic process have the Markov property?
A stochastic process has the Markov property if the conditional probability distribution of future states of the process depends only upon the present state, not on the sequence of events that preceded it.