Search results
Results from the WOW.Com Content Network
A Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. [6]
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.
A stochastic matrix describes a Markov chain X t over a finite state space S with cardinality α.. If the probability of moving from i to j in one time step is Pr(j|i) = P i,j, the stochastic matrix P is given by using P i,j as the i-th row and j-th column element, e.g.,
For a continuous time Markov chain (CTMC) with transition rate matrix, if can be found such that for every pair of states and = holds, then by summing over , the global balance equations are satisfied and is the stationary distribution of the process. [5]
The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. [1] An example of a model for such a field is the Ising model.
A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.
The simplest Markov model is the Markov chain.It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state.
The columns can be labelled "sunny" and "rainy", and the rows can be labelled in the same order. The above matrix as a graph. (P) i j is the probability that, if a given day is of type i, it will be followed by a day of type j. Notice that the rows of P sum to 1: this is because P is a stochastic matrix. [4]