What is the difference between discrete and continuous Markov chain?

A “continuous Markov chain” impels a sense of total convergence to an analytic solution, whereas a discrete Markov chain is unabashedly an approximation.

What is holding time Markov chain?

Holding Times. The Markov property implies the memoryless property for the random time when a Markov process first leaves its initial state. It follows that this random time must have an exponential distribution.

Is time Series A Markov chain?

Usually, time series analysis focuses on dynamics regarding many lags, while the main idea behind Markov chains is to omit the history and focus on the current state. Also, time series analysis has been applied widely, while theoretical approaches for other three kinds are emphasised most of the time.

What is a continuous chain in science?

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. A continuous-time process is called a continuous-time Markov chain (CTMC).

What is time homogeneous Markov chain?

The Markov chain X(t) is time-homogeneous if P(Xn+1 = j|Xn = i) = P(X1 = j|X0 = i), i.e. the transition probabilities do not depend on time n. This says that if it is sunny today, then the chance it will be sunny tomorrow is 0.8, whereas if it is rainy today, then the chance it will be sunny tomorrow is 0.4.

What is a time homogeneous Markov chain?

What is Markov chain in statistics?

A Markov chain presents the random motion of the object. It is a sequence Xn of random variables where each random variable has a transition probability associated with it. Each sequence also has an initial probability distribution π.

What does time-homogeneous mean?

The process is homogeneous in time if the transition probability between two given state values at any two times depends only on the difference between those times.