TRANSITION PROBABILITY MATRIX
Charles François (2004). TRANSITION PROBABILITY MATRIX, International Encyclopedia of Systems and Cybernetics, 2(2): 3625.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 3625 ▶ |
| Object type | Methodology or model |
A matrix which represents all the possible transitions from one state to any other in a Markovian system.
G. PASK describes it as follows: “P is an n.n matrix with{n}2 entries p$_{ij}$ and p$_{ij}$=1 rows and columns corresponding with the states J(t) in a column vector. Each row in the matrix represents the probability distribution obtained by selecting the state in correspondence with this row, as we do in multiplication with the column vector J(t). The state of a Markovian system can be represented as a point in a probability space with n co-ordinates p$_1$, p$_2$… p$_n$ one to each state. This space should not be confused with the phase space with m co-ordinates related to the attributes (1961a, p.122).