At each level the nodes of a recombining tree are indexed from 1 to n (the number of tree nodes at this level), where 1 denotes the lowermost node and n denotes the uppermost node of the tree. The GetProbabilities command returns the list of transition probabilities for the node j at level i of the tree T. This command is related to the GetDescendants command in-as-much as the descendants  returned by GetDescendants and probabilities returned by GetProbabilities are ordered correspondingly.

Note that the transition probabilities can be set using the SetProbabilities command.

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

$X≔\mathrm{OrnsteinUhlenbeckProcess}\left(0.1\,1.0\,0.03\,0.3\right)$

$X≔\mathrm{\_X0}$

$T≔\mathrm{ShortRateTree}\left(X\,4\,10\right)$

$T≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{TreePlot}\left(T\,\mathrm{thickness}=2\,\mathrm{gridlines}=\mathrm{true}\right)$

$\mathrm{GetDescendants}\left(T\,3\,3\right)$

$\left[3\,4\,5\right]$

$\mathrm{GetProbabilities}\left(T\,3\,3\right)$

$\left[0.1507749899\,0.6655866667\,0.1836383434\right]$

$T≔\mathrm{TrinomialTree}\left(5\,⟨1\,2\,3\,4\,5\,6\,7⟩\right)$

$T≔\mathbf{module}\left(\right)\mathbf{end\; module}$

$\mathrm{GetProbabilities}\left(T\,3\,3\right)$

$\left[0.3333333333\,0.3333333334\,0.3333333333\right]$

$\mathrm{SetProbabilities}\left(T\,3\,3\,\left[0.5\,0.2\,0.3\right]\right)$

$\mathrm{GetProbabilities}\left(T\,3\,3\right)$

$\left[0.5000000000\,0.2000000000\,0.3000000000\right]$

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

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