Generating a random walks

### 20.4.25 Generating a random walks

The randmarkov command generates random walks or creates stochastic matrices.

- To generate a random walk, randmarkov takes two arguments:
  - M, a transition matrix for a Markov chain.
  - i0, an initial state.
  - n, a positive integer.
- randmarkov(M,i0,n) returns a a random walk (given as a vector) starting at i0 and taking n random steps, where each step is a transition with probabilities given by M.
- To create a stochastic matrix, randmarkov takes two arguments:
  - v, a vector of length p.
  - i0, the number of transient states.
- randmatrix(v,i0) returns a stochastic matrix with p recurrent loops (given by v) and i0 transient states.

#### Examples

randmarkov([[0,1/2,0,1/2],[0,1,0,0],[1/4,1/4,1/4,1/4],[0,0,1/2,1/2]],2,10)

| ⎡ ⎣ | 2,3,2,0,3,2,2,0,3,2,0 | ⎤ ⎦

randmarkov([1,2],2)

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ |
1.0 | 0.0 | 0.0 | 0.0 | 0.0
0.0 | 0.289031975209 | 0.710968024791 | 0.0 | 0.0
0.0 | 0.46230383289 | 0.53769616711 | 0.0 | 0.0
0.259262238137 | 0.149948861946 | 0.143448150524 | 0.242132758802 | 0.205207990592
0.231568633749 | 0.145429586345 | 0.155664673778 | 0.282556511895 | 0.184780594232
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦