A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix.

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## How do you define a continuous-time Markov chain?

A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix.

**What is the difference between discrete and continuous Markov chain?**

This is discrete because changes to the system state can only happen on someone’s turn. A continuous-time Markov chain is one in which changes to the system can happen at any time along a continuous interval.

### Is Markov chain time invariant?

Definition 3 (Time Invariant Markov Chain) Markov Chain is time-invariant if Pr[Xn = a|Xn−1 = b] = Pr[Xn+l = a|Xn+l−1 = b], ∀n, l, a, b ∈ Ω. Time invariant Markov chain can be specified by distribution on X0 and probability transition matrix P = [Pij], where Pij = Pr[X2 = j|X1 = i].

**What is a continuous chain in science?**

In other words, a continuous-time Markov chain is a stochastic process that moves from state to state in accordance with a (discrete-time) Markov chain, but is such that the amount of time it spends in each state, before proceeding to the next state, is exponentially distributed.

#### How do you calculate holding time?

Record the holding time….Holding time for milk = T(Mv)/Wv) (by volume), in which:

- T = average holding time for water.
- Mv = average time required to deliver a measured volume of product.
- Wv = average time required to deliver an equal volume of water.

**What is the difference between discrete and continuous decision?**

The key differences are: Discrete data is the type of data that has clear spaces between values. Continuous data is data that falls in a constant sequence. Discrete data is countable while continuous — measurable.

## What is discrete and chain?

Definition. A discrete-time Markov chain is a sequence of random variables. with the Markov property, namely that the probability of moving to the next state depends only on the present state and not on the previous states: if both conditional probabilities are well defined, that is, if.

**How do you simulate a Markov process?**

Simulating from a Markov Chain One can simulate from a Markov chain by noting that the collection of moves from any given state (the corresponding row in the probability matrix) form a multinomial distribution. One can thus simulate from a Markov Chain by simulating from a multinomial distribution.

### What is a Markov simulator?

A Markov chain is a probabilistic model describing a system that changes from state to state, and in which the probability of the system being in a certain state at a certain time step depends only on the state of the preceding time step.