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The MarkovChain command creates a new finite state Markov chain.

The parameter P is the transition matrix; it must be a square matrix (see Matrix ) of size $d$, where $d$ is the number of states in the Markov chain. The value $P_{i,j}$ defines the probability of moving from state $j$ to state $i$.

The parameter S is a vector containing values for all possible states of the process.

The parameter n is the number of states per year. This process can only be simulated with $m=nk$ time steps per year, where $k$ is a positive integer. Assume for example that $X$ is a finite state Markov chain with $3$ states per year. If we simulate the process $X$ on the interval $0..2$ with 12 time steps, then the state change can occur only at steps $2$, $4$, $6$, $8$, and $10$.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$P≔⟨⟨0.5\,0.5⟩|⟨0.2\,0.8⟩⟩$

$P≔\left[\begin{array}{cc}0.5& 0.2\\ 0.5& 0.8\end{array}\right]$

$X≔\mathrm{MarkovChain}\left(P\,⟨1.0\,2.0⟩\,1\,5\right)$

$X≔\mathrm{\_X0}$

$\mathrm{SamplePath}\left(X\left(t\right)\,t=0..2\,\mathrm{timesteps}=10\,\mathrm{replications}=10\right)$

$\begin{array}{c}\left[\begin{array}{ccccccccccc}1.& 1.& 1.& 1.& 1.& 1.& 1.& 1.& 2.& 2.& \dots \\ 1.& 1.& 2.& 2.& 1.& 1.& 1.& 1.& 2.& 2.& \dots \\ 1.& 1.& 2.& 2.& 2.& 2.& 2.& 2.& 2.& 1.& \dots \\ 1.& 2.& 1.& 1.& 2.& 2.& 1.& 1.& 2.& 2.& \dots \\ 1.& 2.& 2.& 2.& 2.& 2.& 1.& 2.& 2.& 2.& \dots \\ 1.& 1.& 2.& 2.& 2.& 2.& 2.& 2.& 2.& 2.& \dots \\ 1.& 2.& 1.& 2.& 2.& 1.& 2.& 2.& 2.& 1.& \dots \\ 1.& 1.& 1.& 1.& 1.& 2.& 2.& 2.& 2.& 2.& \dots \\ 1.& 2.& 2.& 1.& 2.& 2.& 2.& 2.& 2.& 2.& \dots \\ 1.& 2.& 2.& 2.& 2.& 1.& 2.& 2.& 2.& 2.& \dots \end{array}\right]\\ \text{10 × 11 Array}\end{array}$

$\mathrm{SamplePath}\left(X\left(t\right)\,t=0..2\,\mathrm{timesteps}=12\,\mathrm{replications}=10\right)$

Error, (in Finance:-SamplePath) update time .200000000000000011 does not belong to the time grid

The Finance[MarkovChain] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15 .