Which is the best definition of a 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). A discrete-time Markov chain involves a system which is in a certain state at each step, with the state changing randomly between steps.
How to simulate from a Markov chain in Python?
One can thus simulate from a Markov Chain by simulating from a multinomial distribution. One way to simulate from a multinomial distribution is to divide a line of length 1 into intervals proportional to the probabilities, and then picking an interval based on a uniform random number between 0 and 1.
What do you mean by discrete time Markov chain?
Discrete Time Markov chain. A discrete-time Markov chain involves a system which is in a certain state at each step, with the state changing randomly between steps. The steps are often thought of as moments in time (But you might as well refer to physical distance or any other discrete measurement).
Based on the previous definition, we can now define “homogenous discrete time Markov chains” (that will be denoted “Markov chains” for simplicity in the following). A Markov chain is a Markov process with discrete time and discrete state space.
What is the transition matrix in a Markov chain?
If a Markov chain consists of k states, the transition matrix is the k by k matrix (a table of numbers) whose entries record the probability of moving from each state to another state (in decimal form, rather than percentage). The rows of the matrix correspond to the current state, and columns correspond to the next state.
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.
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.